Sample records for approximate optimal control

  1. Finite element approximation of an optimal control problem for the von Karman equations

    NASA Technical Reports Server (NTRS)

    Hou, L. Steven; Turner, James C.

    1994-01-01

    This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

  2. Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

    2013-01-01

    This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

  3. Finite dimensional approximation of a class of constrained nonlinear optimal control problems

    NASA Technical Reports Server (NTRS)

    Gunzburger, Max D.; Hou, L. S.

    1994-01-01

    An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

  4. Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers

    NASA Astrophysics Data System (ADS)

    Kim, Sung-Woo; Park, Sang-Young; Park, Chandeok

    2016-01-01

    In this study, a neuro-fuzzy controller (NFC) was developed for spacecraft attitude control to mitigate large computational load of the state-dependent Riccati equation (SDRE) controller. The NFC was developed by training a neuro-fuzzy network to approximate the SDRE controller. The stability of the NFC was numerically verified using a Lyapunov-based method, and the performance of the controller was analyzed in terms of approximation ability, steady-state error, cost, and execution time. The simulations and test results indicate that the developed NFC efficiently approximates the SDRE controller, with asymptotic stability in a bounded region of angular velocity encompassing the operational range of rapid-attitude maneuvers. In addition, it was shown that an approximated optimal feedback controller can be designed successfully through neuro-fuzzy approximation of the optimal open-loop controller.

  5. Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

    PubMed

    Liu, Derong; Li, Hongliang; Wang, Ding

    2015-06-01

    In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

  6. Difference equation state approximations for nonlinear hereditary control problems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1982-01-01

    Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

  7. Difference equation state approximations for nonlinear hereditary control problems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1984-01-01

    Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

  8. Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances.

    PubMed

    Zhang, Huaguang; Qu, Qiuxia; Xiao, Geyang; Cui, Yang

    2018-06-01

    Based on integral sliding mode and approximate dynamic programming (ADP) theory, a novel optimal guaranteed cost sliding mode control is designed for constrained-input nonlinear systems with matched and unmatched disturbances. When the system moves on the sliding surface, the optimal guaranteed cost control problem of sliding mode dynamics is transformed into the optimal control problem of a reformulated auxiliary system with a modified cost function. The ADP algorithm based on single critic neural network (NN) is applied to obtain the approximate optimal control law for the auxiliary system. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors. In addition, the derived approximate optimal control is verified to guarantee the sliding mode dynamics system to be stable in the sense of uniform ultimate boundedness. Some simulation results are presented to verify the feasibility of the proposed control scheme.

  9. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  10. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

    We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

  11. Approximate approach for optimization space flights with a low thrust on the basis of sufficient optimality conditions

    NASA Astrophysics Data System (ADS)

    Salmin, Vadim V.

    2017-01-01

    Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important, as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Author proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.

  12. Spline approximations for nonlinear hereditary control systems

    NASA Technical Reports Server (NTRS)

    Daniel, P. L.

    1982-01-01

    A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

  13. Approximate dynamic programming for optimal stationary control with control-dependent noise.

    PubMed

    Jiang, Yu; Jiang, Zhong-Ping

    2011-12-01

    This brief studies the stochastic optimal control problem via reinforcement learning and approximate/adaptive dynamic programming (ADP). A policy iteration algorithm is derived in the presence of both additive and multiplicative noise using Itô calculus. The expectation of the approximated cost matrix is guaranteed to converge to the solution of some algebraic Riccati equation that gives rise to the optimal cost value. Moreover, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, a numerical example is given to illustrate the efficiency of the proposed ADP methodology.

  14. Parametric optimal control of uncertain systems under an optimistic value criterion

    NASA Astrophysics Data System (ADS)

    Li, Bo; Zhu, Yuanguo

    2018-01-01

    It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.

  15. Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1984-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  16. Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  17. Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

    PubMed

    Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

    2011-12-01

    In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

  18. Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

    PubMed

    Wei, Qinglai; Li, Benkai; Song, Ruizhuo

    2018-04-01

    In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

  19. Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

    PubMed

    Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

    2013-12-01

    In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

  20. Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Bernstein, Dennis S.; Rosen, I. G.

    1988-01-01

    In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

  1. Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

    PubMed

    Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

    2018-02-01

    Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

  2. Approximate optimal tracking control for near-surface AUVs with wave disturbances

    NASA Astrophysics Data System (ADS)

    Yang, Qing; Su, Hao; Tang, Gongyou

    2016-10-01

    This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.

  3. Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Wang, C.

    1989-01-01

    A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

  4. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au; Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem ofmore » optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.« less

  5. Piecewise linear approximation for hereditary control problems

    NASA Technical Reports Server (NTRS)

    Propst, Georg

    1987-01-01

    Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

  6. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1987-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  7. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1988-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  8. Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

  9. Neural dynamic programming and its application to control systems

    NASA Astrophysics Data System (ADS)

    Seong, Chang-Yun

    There are few general practical feedback control methods for nonlinear MIMO (multi-input-multi-output) systems, although such methods exist for their linear counterparts. Neural Dynamic Programming (NDP) is proposed as a practical design method of optimal feedback controllers for nonlinear MIMO systems. NDP is an offspring of both neural networks and optimal control theory. In optimal control theory, the optimal solution to any nonlinear MIMO control problem may be obtained from the Hamilton-Jacobi-Bellman equation (HJB) or the Euler-Lagrange equations (EL). The two sets of equations provide the same solution in different forms: EL leads to a sequence of optimal control vectors, called Feedforward Optimal Control (FOC); HJB yields a nonlinear optimal feedback controller, called Dynamic Programming (DP). DP produces an optimal solution that can reject disturbances and uncertainties as a result of feedback. Unfortunately, computation and storage requirements associated with DP solutions can be problematic, especially for high-order nonlinear systems. This dissertation presents an approximate technique for solving the DP problem based on neural network techniques that provides many of the performance benefits (e.g., optimality and feedback) of DP and benefits from the numerical properties of neural networks. We formulate neural networks to approximate optimal feedback solutions whose existence DP justifies. We show the conditions under which NDP closely approximates the optimal solution. Finally, we introduce the learning operator characterizing the learning process of the neural network in searching the optimal solution. The analysis of the learning operator provides not only a fundamental understanding of the learning process in neural networks but also useful guidelines for selecting the number of weights of the neural network. As a result, NDP finds---with a reasonable amount of computation and storage---the optimal feedback solutions to nonlinear MIMO control problems that would be very difficult to solve with DP. NDP was demonstrated on several applications such as the lateral autopilot logic for a Boeing 747, the minimum fuel control of a double-integrator plant with bounded control, the backward steering of a two-trailer truck, and the set-point control of a two-link robot arm.

  10. Multidisciplinary design optimization of aircraft wing structures with aeroelastic and aeroservoelastic constraints

    NASA Astrophysics Data System (ADS)

    Jung, Sang-Young

    Design procedures for aircraft wing structures with control surfaces are presented using multidisciplinary design optimization. Several disciplines such as stress analysis, structural vibration, aerodynamics, and controls are considered simultaneously and combined for design optimization. Vibration data and aerodynamic data including those in the transonic regime are calculated by existing codes. Flutter analyses are performed using those data. A flutter suppression method is studied using control laws in the closed-loop flutter equation. For the design optimization, optimization techniques such as approximation, design variable linking, temporary constraint deletion, and optimality criteria are used. Sensitivity derivatives of stresses and displacements for static loads, natural frequency, flutter characteristics, and control characteristics with respect to design variables are calculated for an approximate optimization. The objective function is the structural weight. The design variables are the section properties of the structural elements and the control gain factors. Existing multidisciplinary optimization codes (ASTROS* and MSC/NASTRAN) are used to perform single and multiple constraint optimizations of fully built up finite element wing structures. Three benchmark wing models are developed and/or modified for this purpose. The models are tested extensively.

  11. Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

  12. Training Recurrent Neural Networks With the Levenberg-Marquardt Algorithm for Optimal Control of a Grid-Connected Converter.

    PubMed

    Fu, Xingang; Li, Shuhui; Fairbank, Michael; Wunsch, Donald C; Alonso, Eduardo

    2015-09-01

    This paper investigates how to train a recurrent neural network (RNN) using the Levenberg-Marquardt (LM) algorithm as well as how to implement optimal control of a grid-connected converter (GCC) using an RNN. To successfully and efficiently train an RNN using the LM algorithm, a new forward accumulation through time (FATT) algorithm is proposed to calculate the Jacobian matrix required by the LM algorithm. This paper explores how to incorporate FATT into the LM algorithm. The results show that the combination of the LM and FATT algorithms trains RNNs better than the conventional backpropagation through time algorithm. This paper presents an analytical study on the optimal control of GCCs, including theoretically ideal optimal and suboptimal controllers. To overcome the inapplicability of the optimal GCC controller under practical conditions, a new RNN controller with an improved input structure is proposed to approximate the ideal optimal controller. The performance of an ideal optimal controller and a well-trained RNN controller was compared in close to real-life power converter switching environments, demonstrating that the proposed RNN controller can achieve close to ideal optimal control performance even under low sampling rate conditions. The excellent performance of the proposed RNN controller under challenging and distorted system conditions further indicates the feasibility of using an RNN to approximate optimal control in practical applications.

  13. Neural network-based optimal adaptive output feedback control of a helicopter UAV.

    PubMed

    Nodland, David; Zargarzadeh, Hassan; Jagannathan, Sarangapani

    2013-07-01

    Helicopter unmanned aerial vehicles (UAVs) are widely used for both military and civilian operations. Because the helicopter UAVs are underactuated nonlinear mechanical systems, high-performance controller design for them presents a challenge. This paper introduces an optimal controller design via an output feedback for trajectory tracking of a helicopter UAV, using a neural network (NN). The output-feedback control system utilizes the backstepping methodology, employing kinematic and dynamic controllers and an NN observer. The online approximator-based dynamic controller learns the infinite-horizon Hamilton-Jacobi-Bellman equation in continuous time and calculates the corresponding optimal control input by minimizing a cost function, forward-in-time, without using the value and policy iterations. Optimal tracking is accomplished by using a single NN utilized for the cost function approximation. The overall closed-loop system stability is demonstrated using Lyapunov analysis. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control design for trajectory tracking.

  14. Approximated analytical solution to an Ebola optimal control problem

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

    2016-11-01

    An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

  15. A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

    NASA Technical Reports Server (NTRS)

    Milman, M. H.

    1985-01-01

    A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

  16. Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

    PubMed

    Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

    2018-04-01

    This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

  17. Finding Optimal Gains In Linear-Quadratic Control Problems

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.; Scheid, Robert E., Jr.

    1990-01-01

    Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

  18. Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation

    NASA Technical Reports Server (NTRS)

    Clifton, C.; Homaifax, A.; Bikdash, M.

    1997-01-01

    This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.

  19. Factorization and reduction methods for optimal control of distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Burns, J. A.; Powers, R. K.

    1985-01-01

    A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

  20. Unified control/structure design and modeling research

    NASA Technical Reports Server (NTRS)

    Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

    1986-01-01

    To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

  1. Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

    NASA Astrophysics Data System (ADS)

    Lv, Yongfeng; Na, Jing; Yang, Qinmin; Wu, Xing; Guo, Yu

    2016-01-01

    An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

  2. Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

    NASA Astrophysics Data System (ADS)

    Wang, Jing; Yang, Tianyu; Staskevich, Gennady; Abbe, Brian

    2017-04-01

    This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton-Jacobi-Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.

  3. A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

    DOE PAGES

    Kouri, Drew Philip

    2017-12-19

    In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

  4. Legendre spectral-collocation method for solving some types of fractional optimal control problems

    PubMed Central

    Sweilam, Nasser H.; Al-Ajami, Tamer M.

    2014-01-01

    In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937

  5. Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

  6. The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

    NASA Astrophysics Data System (ADS)

    Chen, Shuhong; Tan, Zhong

    2007-11-01

    In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

  7. Optimal birth control of age-dependent competitive species

    NASA Astrophysics Data System (ADS)

    He, Ze-Rong

    2005-05-01

    We study optimal birth policies for two age-dependent populations in a competing system, which is controlled by fertilities. New results on problems with free final time and integral phase constraints are presented, and the approximate controllability of system is discussed.

  8. Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

    PubMed

    Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

    2015-11-01

    The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

  9. Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

    NASA Astrophysics Data System (ADS)

    Marcozzi, Michael D.

    2008-12-01

    We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.

  10. Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.

    PubMed

    Narayanan, Vignesh; Jagannathan, Sarangapani

    2017-06-08

    This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.

  11. Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi

    1987-01-01

    The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

  12. A novel model of motor learning capable of developing an optimal movement control law online from scratch.

    PubMed

    Shimansky, Yury P; Kang, Tao; He, Jiping

    2004-02-01

    A computational model of a learning system (LS) is described that acquires knowledge and skill necessary for optimal control of a multisegmental limb dynamics (controlled object or CO), starting from "knowing" only the dimensionality of the object's state space. It is based on an optimal control problem setup different from that of reinforcement learning. The LS solves the optimal control problem online while practicing the manipulation of CO. The system's functional architecture comprises several adaptive components, each of which incorporates a number of mapping functions approximated based on artificial neural nets. Besides the internal model of the CO's dynamics and adaptive controller that computes the control law, the LS includes a new type of internal model, the minimal cost (IM(mc)) of moving the controlled object between a pair of states. That internal model appears critical for the LS's capacity to develop an optimal movement trajectory. The IM(mc) interacts with the adaptive controller in a cooperative manner. The controller provides an initial approximation of an optimal control action, which is further optimized in real time based on the IM(mc). The IM(mc) in turn provides information for updating the controller. The LS's performance was tested on the task of center-out reaching to eight randomly selected targets with a 2DOF limb model. The LS reached an optimal level of performance in a few tens of trials. It also quickly adapted to movement perturbations produced by two different types of external force field. The results suggest that the proposed design of a self-optimized control system can serve as a basis for the modeling of motor learning that includes the formation and adaptive modification of the plan of a goal-directed movement.

  13. Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

    NASA Technical Reports Server (NTRS)

    Patten, W. N.; Robertshaw, H. H.; Pierpont, D.; Wynn, R. H.

    1989-01-01

    A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

  14. Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

    1985-01-01

    The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

  15. An approximation theory for nonlinear partial differential equations with applications to identification and control

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  16. Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.

    PubMed

    Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai

    2015-07-01

    The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.

  17. Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

    We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

  18. Precision of Sensitivity in the Design Optimization of Indeterminate Structures

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.

    2006-01-01

    Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

  19. Event-Triggered Distributed Control of Nonlinear Interconnected Systems Using Online Reinforcement Learning With Exploration.

    PubMed

    Narayanan, Vignesh; Jagannathan, Sarangapani

    2017-09-07

    In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.

  20. Gradient Optimization for Analytic conTrols - GOAT

    NASA Astrophysics Data System (ADS)

    Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank

    Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.

  1. Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

    NASA Astrophysics Data System (ADS)

    Yang, Xiong; Liu, Derong; Wang, Ding

    2014-03-01

    In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.

  2. Alternatives for jet engine control

    NASA Technical Reports Server (NTRS)

    Sain, M. K.

    1984-01-01

    The technical progress of researches on alternatives for jet engine control is reported. Extensive numerical testing is included. It is indicated that optimal inputs contribute significantly to the process of calculating tensor approximations for nonlinear systems, and that the resulting approximations may be order-reduced in a systematic way.

  3. Modeling and control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Mingori, D. L.

    1988-01-01

    This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

  4. Finite-Dimensional Representations for Controlled Diffusions with Delay

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

    2015-02-15

    We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

  5. Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks.

    PubMed

    Li, Zhijun; Ge, Shuzhi Sam; Liu, Sibang

    2014-08-01

    This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

  6. Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

    PubMed

    Wang, Jun-Sheng; Yang, Guang-Hong

    2017-07-25

    This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

  7. A policy iteration approach to online optimal control of continuous-time constrained-input systems.

    PubMed

    Modares, Hamidreza; Naghibi Sistani, Mohammad-Bagher; Lewis, Frank L

    2013-09-01

    This paper is an effort towards developing an online learning algorithm to find the optimal control solution for continuous-time (CT) systems subject to input constraints. The proposed method is based on the policy iteration (PI) technique which has recently evolved as a major technique for solving optimal control problems. Although a number of online PI algorithms have been developed for CT systems, none of them take into account the input constraints caused by actuator saturation. In practice, however, ignoring these constraints leads to performance degradation or even system instability. In this paper, to deal with the input constraints, a suitable nonquadratic functional is employed to encode the constraints into the optimization formulation. Then, the proposed PI algorithm is implemented on an actor-critic structure to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with this nonquadratic cost functional in an online fashion. That is, two coupled neural network (NN) approximators, namely an actor and a critic are tuned online and simultaneously for approximating the associated HJB solution and computing the optimal control policy. The critic is used to evaluate the cost associated with the current policy, while the actor is used to find an improved policy based on information provided by the critic. Convergence to a close approximation of the HJB solution as well as stability of the proposed feedback control law are shown. Simulation results of the proposed method on a nonlinear CT system illustrate the effectiveness of the proposed approach. Copyright © 2013 ISA. All rights reserved.

  8. Structural optimization: Status and promise

    NASA Astrophysics Data System (ADS)

    Kamat, Manohar P.

    Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

  9. Computational alternatives to obtain time optimal jet engine control. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Basso, R. J.; Leake, R. J.

    1976-01-01

    Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

  10. Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.; Wall, Johnm W.

    2011-01-01

    In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

  11. Time-optimal control with finite bandwidth

    NASA Astrophysics Data System (ADS)

    Hirose, M.; Cappellaro, P.

    2018-04-01

    Time-optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite response time of the control apparatus, prevent the implementation of theoretical time-optimal control. Here we present a method to achieve time-optimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from time-optimal control theory to design driving protocols that can be implemented with realistic, finite-bandwidth control fields, and we find a relationship between bandwidth limitations and achievable control fidelity.

  12. Neural-Network-Based Robust Optimal Tracking Control for MIMO Discrete-Time Systems With Unknown Uncertainty Using Adaptive Critic Design.

    PubMed

    Liu, Lei; Wang, Zhanshan; Zhang, Huaguang

    2018-04-01

    This paper is concerned with the robust optimal tracking control strategy for a class of nonlinear multi-input multi-output discrete-time systems with unknown uncertainty via adaptive critic design (ACD) scheme. The main purpose is to establish an adaptive actor-critic control method, so that the cost function in the procedure of dealing with uncertainty is minimum and the closed-loop system is stable. Based on the neural network approximator, an action network is applied to generate the optimal control signal and a critic network is used to approximate the cost function, respectively. In contrast to the previous methods, the main features of this paper are: 1) the ACD scheme is integrated into the controllers to cope with the uncertainty and 2) a novel cost function, which is not in quadric form, is proposed so that the total cost in the design procedure is reduced. It is proved that the optimal control signals and the tracking errors are uniformly ultimately bounded even when the uncertainty exists. Finally, a numerical simulation is developed to show the effectiveness of the present approach.

  13. Model-Free Optimal Tracking Control via Critic-Only Q-Learning.

    PubMed

    Luo, Biao; Liu, Derong; Huang, Tingwen; Wang, Ding

    2016-10-01

    Model-free control is an important and promising topic in control fields, which has attracted extensive attention in the past few years. In this paper, we aim to solve the model-free optimal tracking control problem of nonaffine nonlinear discrete-time systems. A critic-only Q-learning (CoQL) method is developed, which learns the optimal tracking control from real system data, and thus avoids solving the tracking Hamilton-Jacobi-Bellman equation. First, the Q-learning algorithm is proposed based on the augmented system, and its convergence is established. Using only one neural network for approximating the Q-function, the CoQL method is developed to implement the Q-learning algorithm. Furthermore, the convergence of the CoQL method is proved with the consideration of neural network approximation error. With the convergent Q-function obtained from the CoQL method, the adaptive optimal tracking control is designed based on the gradient descent scheme. Finally, the effectiveness of the developed CoQL method is demonstrated through simulation studies. The developed CoQL method learns with off-policy data and implements with a critic-only structure, thus it is easy to realize and overcome the inadequate exploration problem.

  14. On l(1): Optimal decentralized performance

    NASA Technical Reports Server (NTRS)

    Sourlas, Dennis; Manousiouthakis, Vasilios

    1993-01-01

    In this paper, the Manousiouthakis parametrization of all decentralized stabilizing controllers is employed in mathematically formulating the l(sup 1) optimal decentralized controller synthesis problem. The resulting optimization problem is infinite dimensional and therefore not directly amenable to computations. It is shown that finite dimensional optimization problems that have value arbitrarily close to the infinite dimensional one can be constructed. Based on this result, an algorithm that solves the l(sup 1) decentralized performance problems is presented. A global optimization approach to the solution of the infinite dimensional approximating problems is also discussed.

  15. Some optimal considerations in attitude control systems. [evaluation of value of relative weighting between time and fuel for relay control law

    NASA Technical Reports Server (NTRS)

    Boland, J. S., III

    1973-01-01

    The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

  16. A computational algorithm for spacecraft control and momentum management

    NASA Technical Reports Server (NTRS)

    Dzielski, John; Bergmann, Edward; Paradiso, Joseph

    1990-01-01

    Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

  17. Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

    2017-06-01

    In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

  18. Advanced launch system trajectory optimization using suboptimal control

    NASA Technical Reports Server (NTRS)

    Shaver, Douglas A.; Hull, David G.

    1993-01-01

    The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations.

  19. Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

    NASA Astrophysics Data System (ADS)

    Mansfield, Christopher M.; Shoemaker, Christine A.

    1999-05-01

    This paper extends earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequately approximated by the simpler confined-aquifer analysis.

  20. Optimal Power Flow for Distribution Systems under Uncertain Forecasts: Preprint

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

    2016-12-01

    The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

  1. Adaptive surrogate model based multi-objective transfer trajectory optimization between different libration points

    NASA Astrophysics Data System (ADS)

    Peng, Haijun; Wang, Wei

    2016-10-01

    An adaptive surrogate model-based multi-objective optimization strategy that combines the benefits of invariant manifolds and low-thrust control toward developing a low-computational-cost transfer trajectory between libration orbits around the L1 and L2 libration points in the Sun-Earth system has been proposed in this paper. A new structure for a multi-objective transfer trajectory optimization model that divides the transfer trajectory into several segments and gives the dominations for invariant manifolds and low-thrust control in different segments has been established. To reduce the computational cost of multi-objective transfer trajectory optimization, a mixed sampling strategy-based adaptive surrogate model has been proposed. Numerical simulations show that the results obtained from the adaptive surrogate-based multi-objective optimization are in agreement with the results obtained using direct multi-objective optimization methods, and the computational workload of the adaptive surrogate-based multi-objective optimization is only approximately 10% of that of direct multi-objective optimization. Furthermore, the generating efficiency of the Pareto points of the adaptive surrogate-based multi-objective optimization is approximately 8 times that of the direct multi-objective optimization. Therefore, the proposed adaptive surrogate-based multi-objective optimization provides obvious advantages over direct multi-objective optimization methods.

  2. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

    The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

  3. A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

    NASA Astrophysics Data System (ADS)

    Song, Rui-Zhuo; Xiao, Wen-Dong; Wei, Qing-Lai

    2014-05-01

    We develop an online adaptive dynamic programming (ADP) based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.

  4. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  5. OPTRAN- OPTIMAL LOW THRUST ORBIT TRANSFERS

    NASA Technical Reports Server (NTRS)

    Breakwell, J. V.

    1994-01-01

    OPTRAN is a collection of programs that solve the problem of optimal low thrust orbit transfers between non-coplanar circular orbits for spacecraft with chemical propulsion systems. The programs are set up to find Hohmann-type solutions, with burns near the perigee and apogee of the transfer orbit. They will solve both fairly long burn-arc transfers and "divided-burn" transfers. Program modeling includes a spherical earth gravity model and propulsion system models for either constant thrust or constant acceleration. The solutions obtained are optimal with respect to fuel use: i.e., final mass of the spacecraft is maximized with respect to the controls. The controls are the direction of thrust and the thrust on/off times. Two basic types of programs are provided in OPTRAN. The first type is for "exact solution" which results in complete, exact tkme-histories. The exact spacecraft position, velocity, and optimal thrust direction are given throughout the maneuver, as are the optimal thrust switch points, the transfer time, and the fuel costs. Exact solution programs are provided in two versions for non-coplanar transfers and in a fast version for coplanar transfers. The second basic type is for "approximate solutions" which results in approximate information on the transfer time and fuel costs. The approximate solution is used to estimate initial conditions for the exact solution. It can be used in divided-burn transfers to find the best number of burns with respect to time. The approximate solution is useful by itself in relatively efficient, short burn-arc transfers. These programs are written in FORTRAN 77 for batch execution and have been implemented on a DEC VAX series computer with the largest program having a central memory requirement of approximately 54K of 8 bit bytes. The OPTRAN program were developed in 1983.

  6. Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming.

    PubMed

    Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan

    2011-12-01

    In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.

  7. Active vibration control for flexible rotor by optimal direct-output feedback control

    NASA Technical Reports Server (NTRS)

    Nonami, Kenzou; Dirusso, Eliseo; Fleming, David P.

    1989-01-01

    Experimental research tests were performed to actively control the rotor vibrations of a flexible rotor mounted on flexible bearing supports. The active control method used in the tests is called optimal direct-output feedback control. This method uses four electrodynamic actuators to apply control forces directly to the bearing housings in order to achieve effective vibration control of the rotor. The force actuators are controlled by an analog controller that accepts rotor displacement as input. The controller is programmed with experimentally determined feedback coefficients; the output is a control signal to the force actuators. The tests showed that this active control method reduced the rotor resonance peaks due to unbalance from approximately 250 micrometers down to approximately 25 micrometers (essentially runout level). The tests were conducted over a speed range from 0 to 10,000 rpm; the rotor system had nine critical speeds within this speed range. The method was effective in significantly reducing the rotor vibration for all of the vibration modes and critical speeds.

  8. Active vibration control for flexible rotor by optimal direct-output feedback control

    NASA Technical Reports Server (NTRS)

    Nonami, K.; Dirusso, E.; Fleming, D. P.

    1989-01-01

    Experimental research tests were performed to actively control the rotor vibrations of a flexible rotor mounted on flexible bearing supports. The active control method used in the tests is called optimal direct-output feedback control. This method uses four electrodynamic actuators to apply control forces directly to the bearing housings in order to achieve effective vibration control of the rotor. The force actuators are controlled by an analog controller that accepts rotor displacement as input. The controller is programmed with experimentally determined feedback coefficients; the output is a control signal to the force actuators. The tests showed that this active control method reduced the rotor resonance peaks due to unbalance from approximately 250 microns down to approximately 25 microns (essentially runout level). The tests were conducted over a speed range from 0 to 10,000 rpm; the rotor system had nine critical speeds within this speed range. The method was effective in significantly reducing the rotor vibration for all of the vibration modes and critical speeds.

  9. Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

    NASA Astrophysics Data System (ADS)

    Bania, Piotr; Baranowski, Jerzy

    2018-02-01

    Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

  10. Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    DallAnese, Emiliano; Baker, Kyri; Summers, Tyler

    This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrarymore » distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.« less

  11. Optimal and Approximately Optimal Control Policies for Queues in Heavy Traffic,

    DTIC Science & Technology

    1987-03-01

    optimal and ’nearly optimal’ control problems for the open queueing networks in heavy traffic of the type dealt with in the fundamental papers of Reiman ...then the covariance is precisely that obtained by Reiman [1] (with a different notation used there). It is evident from (4.4) and the cited...wU’ ’U, d A K . " -50- References [1] M.I. Reiman , "Open queueing networks in heavy traffic", Math. of Operations Research, 9, 1984, p. 441-458. [2] J

  12. Neural dynamic optimization for control systems. I. Background.

    PubMed

    Seong, C Y; Widrow, B

    2001-01-01

    The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the background and motivations for the development of NDO, while the two other subsequent papers of this topic present the theory of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

  13. Neural dynamic optimization for control systems.III. Applications.

    PubMed

    Seong, C Y; Widrow, B

    2001-01-01

    For pt.II. see ibid., p. 490-501. The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper demonstrates NDO with several applications including control of autonomous vehicles and of a robot-arm, while the two other companion papers of this topic describes the background for the development of NDO and present the theory of the method, respectively.

  14. Neural dynamic optimization for control systems.II. Theory.

    PubMed

    Seong, C Y; Widrow, B

    2001-01-01

    The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the theory of NDO, while the two other companion papers of this topic explain the background for the development of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

  15. Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design.

    PubMed

    Wang, Zhanshan; Liu, Lei; Wu, Yanming; Zhang, Huaguang

    2018-06-01

    This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

  16. Direct SQP-methods for solving optimal control problems with delays

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Goellmann, L.; Bueskens, C.; Maurer, H.

    The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

  17. Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

    PubMed

    Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

    2017-10-01

    The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

  18. Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

    PubMed

    Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

    2011-01-01

    In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

  19. A nonlinear optimal control approach for chaotic finance dynamics

    NASA Astrophysics Data System (ADS)

    Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

    2017-11-01

    A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

  20. Achieving Consistent Near-Optimal Pattern Recognition Accuracy Using Particle Swarm Optimization to Pre-Train Artificial Neural Networks

    ERIC Educational Resources Information Center

    Nikelshpur, Dmitry O.

    2014-01-01

    Similar to mammalian brains, Artificial Neural Networks (ANN) are universal approximators, capable of yielding near-optimal solutions to a wide assortment of problems. ANNs are used in many fields including medicine, internet security, engineering, retail, robotics, warfare, intelligence control, and finance. "ANNs have a tendency to get…

  1. Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach.

    PubMed

    Liu, Derong; Wang, Ding; Li, Hongliang

    2014-02-01

    In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuous-time nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme.

  2. Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

    PubMed

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

  3. Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

    PubMed Central

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

  4. Strategies for Optimal Control Design of Normal Acceleration Command Following on the F-16

    DTIC Science & Technology

    1992-12-01

    Padd approximation. This approximation has a pole at -40, and introduces a nonminimum phase zero at +40. In deriving the equation for normal acceleration...input signal. The mean not being exactly zero will surface in some simulation plots, but does not alter the point of showing general trends. Also...closer to reality, I will ’know that my goal has been accomplished. My honest belief is that general mixed H2/H.. optimization is the methodology of

  5. A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

    NASA Technical Reports Server (NTRS)

    Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

    1979-01-01

    A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

  6. Multi-disciplinary optimization of aeroservoelastic systems

    NASA Technical Reports Server (NTRS)

    Karpel, Mordechay

    1990-01-01

    Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

  7. Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

    NASA Technical Reports Server (NTRS)

    Karpel, Mordechay

    1992-01-01

    Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

  8. Control of minimum member size in parameter-free structural shape optimization by a medial axis approximation

    NASA Astrophysics Data System (ADS)

    Schmitt, Oliver; Steinmann, Paul

    2018-06-01

    We introduce a manufacturing constraint for controlling the minimum member size in structural shape optimization problems, which is for example of interest for components fabricated in a molding process. In a parameter-free approach, whereby the coordinates of the FE boundary nodes are used as design variables, the challenging task is to find a generally valid definition for the thickness of non-parametric geometries in terms of their boundary nodes. Therefore we use the medial axis, which is the union of all points with at least two closest points on the boundary of the domain. Since the effort for the exact computation of the medial axis of geometries given by their FE discretization highly increases with the number of surface elements we use the distance function instead to approximate the medial axis by a cloud of points. The approximation is demonstrated on three 2D examples. Moreover, the formulation of a minimum thickness constraint is applied to a sensitivity-based shape optimization problem of one 2D and one 3D model.

  9. Control of minimum member size in parameter-free structural shape optimization by a medial axis approximation

    NASA Astrophysics Data System (ADS)

    Schmitt, Oliver; Steinmann, Paul

    2017-09-01

    We introduce a manufacturing constraint for controlling the minimum member size in structural shape optimization problems, which is for example of interest for components fabricated in a molding process. In a parameter-free approach, whereby the coordinates of the FE boundary nodes are used as design variables, the challenging task is to find a generally valid definition for the thickness of non-parametric geometries in terms of their boundary nodes. Therefore we use the medial axis, which is the union of all points with at least two closest points on the boundary of the domain. Since the effort for the exact computation of the medial axis of geometries given by their FE discretization highly increases with the number of surface elements we use the distance function instead to approximate the medial axis by a cloud of points. The approximation is demonstrated on three 2D examples. Moreover, the formulation of a minimum thickness constraint is applied to a sensitivity-based shape optimization problem of one 2D and one 3D model.

  10. Closed loop models for analyzing the effects of simulator characteristics. [digital simulation of human operators

    NASA Technical Reports Server (NTRS)

    Baron, S.; Muralidharan, R.; Kleinman, D. L.

    1978-01-01

    The optimal control model of the human operator is used to develop closed loop models for analyzing the effects of (digital) simulator characteristics on predicted performance and/or workload. Two approaches are considered: the first utilizes a continuous approximation to the discrete simulation in conjunction with the standard optimal control model; the second involves a more exact discrete description of the simulator in a closed loop multirate simulation in which the optimal control model simulates the pilot. Both models predict that simulator characteristics can have significant effects on performance and workload.

  11. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

    NASA Astrophysics Data System (ADS)

    Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu

    2017-10-01

    Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

  12. Optimization and control of perfusion cultures using a viable cell probe and cell specific perfusion rates.

    PubMed

    Dowd, Jason E; Jubb, Anthea; Kwok, K Ezra; Piret, James M

    2003-05-01

    Consistent perfusion culture production requires reliable cell retention and control of feed rates. An on-line cell probe based on capacitance was used to assay viable biomass concentrations. A constant cell specific perfusion rate controlled medium feed rates with a bioreactor cell concentration of approximately 5 x 10(6) cells mL(-1). Perfusion feeding was automatically adjusted based on the cell concentration signal from the on-line biomass sensor. Cell specific perfusion rates were varied over a range of 0.05 to 0.4 nL cell(-1) day(-1). Pseudo-steady-state bioreactor indices (concentrations, cellular rates and yields) were correlated to cell specific perfusion rates investigated to maximize recombinant protein production from a Chinese hamster ovary cell line. The tissue-type plasminogen activator concentration was maximized ( approximately 40 mg L(-1)) at 0.2 nL cell(-1) day(-1). The volumetric protein productivity ( approximately 60 mg L(-1) day(-1) was maximized above 0.3 nL cell(-1) day(-1). The use of cell specific perfusion rates provided a straightforward basis for controlling, modeling and optimizing perfusion cultures.

  13. Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

    NASA Technical Reports Server (NTRS)

    Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.

    2011-01-01

    We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

  14. Optimal False Discovery Rate Control for Dependent Data

    PubMed Central

    Xie, Jichun; Cai, T. Tony; Maris, John; Li, Hongzhe

    2013-01-01

    This paper considers the problem of optimal false discovery rate control when the test statistics are dependent. An optimal joint oracle procedure, which minimizes the false non-discovery rate subject to a constraint on the false discovery rate is developed. A data-driven marginal plug-in procedure is then proposed to approximate the optimal joint procedure for multivariate normal data. It is shown that the marginal procedure is asymptotically optimal for multivariate normal data with a short-range dependent covariance structure. Numerical results show that the marginal procedure controls false discovery rate and leads to a smaller false non-discovery rate than several commonly used p-value based false discovery rate controlling methods. The procedure is illustrated by an application to a genome-wide association study of neuroblastoma and it identifies a few more genetic variants that are potentially associated with neuroblastoma than several p-value-based false discovery rate controlling procedures. PMID:23378870

  15. An approximation function for frequency constrained structural optimization

    NASA Technical Reports Server (NTRS)

    Canfield, R. A.

    1989-01-01

    The purpose is to examine a function for approximating natural frequency constraints during structural optimization. The nonlinearity of frequencies has posed a barrier to constructing approximations for frequency constraints of high enough quality to facilitate efficient solutions. A new function to represent frequency constraints, called the Rayleigh Quotient Approximation (RQA), is presented. Its ability to represent the actual frequency constraint results in stable convergence with effectively no move limits. The objective of the optimization problem is to minimize structural weight subject to some minimum (or maximum) allowable frequency and perhaps subject to other constraints such as stress, displacement, and gage size, as well. A reason for constraining natural frequencies during design might be to avoid potential resonant frequencies due to machinery or actuators on the structure. Another reason might be to satisy requirements of an aircraft or spacecraft's control law. Whatever the structure supports may be sensitive to a frequency band that must be avoided. Any of these situations or others may require the designer to insure the satisfaction of frequency constraints. A further motivation for considering accurate approximations of natural frequencies is that they are fundamental to dynamic response constraints.

  16. Optimal Power Flow Pursuit

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall'Anese, Emiliano; Simonetto, Andrea

    This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of AC optimal power flow (OPF) problems. Particularly, the controllers update the power setpoints based on voltage measurements as well as given (time-varying) OPF targets, and entail elementary operations implementable onto low-cost microcontrollers that accompany power-electronics interfaces of gateways and inverters. The design of the control framework is based on suitable linear approximations of the AC power-flow equations as well as Lagrangian regularization methods. Convergence and OPF-target tracking capabilities of the controllers are analytically established. Overall,more » the proposed method allows to bypass traditional hierarchical setups where feedback control and optimization operate at distinct time scales, and to enable real-time optimization of distribution systems.« less

  17. Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

    NASA Astrophysics Data System (ADS)

    Luy, N. T.

    2018-04-01

    The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

  18. Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nelson, Andrea; Aftosmis, Michael J.; Nemec, Marian; Pulliam, Thomas H.

    2004-01-01

    Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

  19. Boundary control of bidomain equations with state-dependent switching source functions in the ionic model

    NASA Astrophysics Data System (ADS)

    Chamakuri, Nagaiah; Engwer, Christian; Kunisch, Karl

    2014-09-01

    Optimal control for cardiac electrophysiology based on the bidomain equations in conjunction with the Fenton-Karma ionic model is considered. This generic ventricular model approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potentials. However, it is challenging due to the appearance of state-dependent discontinuities in the source terms. A computational framework for the numerical realization of optimal control problems is presented. Essential ingredients are a shape calculus based treatment of the sensitivities of the discontinuous source terms and a marching cubes algorithm to track iso-surface of excitation wavefronts. Numerical results exhibit successful defibrillation by applying an optimally controlled extracellular stimulus.

  20. Optimal control of Formula One car energy recovery systems

    NASA Astrophysics Data System (ADS)

    Limebeer, D. J. N.; Perantoni, G.; Rao, A. V.

    2014-10-01

    The utility of orthogonal collocation methods in the solution of optimal control problems relating to Formula One racing is demonstrated. These methods can be used to optimise driver controls such as the steering, braking and throttle usage, and to optimise vehicle parameters such as the aerodynamic down force and mass distributions. Of particular interest is the optimal usage of energy recovery systems (ERSs). Contemporary kinetic energy recovery systems are studied and compared with future hybrid kinetic and thermal/heat ERSs known as ERS-K and ERS-H, respectively. It is demonstrated that these systems, when properly controlled, can produce contemporary lap time using approximately two-thirds of the fuel required by earlier generation (2013 and prior) vehicles.

  1. Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

    NASA Astrophysics Data System (ADS)

    Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

    2013-09-01

    In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

  2. Optimal Real-time Dispatch for Integrated Energy Systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Firestone, Ryan Michael

    This report describes the development and application of a dispatch optimization algorithm for integrated energy systems (IES) comprised of on-site cogeneration of heat and electricity, energy storage devices, and demand response opportunities. This work is intended to aid commercial and industrial sites in making use of modern computing power and optimization algorithms to make informed, near-optimal decisions under significant uncertainty and complex objective functions. The optimization algorithm uses a finite set of randomly generated future scenarios to approximate the true, stochastic future; constraints are included that prevent solutions to this approximate problem from deviating from solutions to the actual problem.more » The algorithm is then expressed as a mixed integer linear program, to which a powerful commercial solver is applied. A case study of United States Postal Service Processing and Distribution Centers (P&DC) in four cities and under three different electricity tariff structures is conducted to (1) determine the added value of optimal control to a cogeneration system over current, heuristic control strategies; (2) determine the value of limited electric load curtailment opportunities, with and without cogeneration; and (3) determine the trade-off between least-cost and least-carbon operations of a cogeneration system. Key results for the P&DC sites studied include (1) in locations where the average electricity and natural gas prices suggest a marginally profitable cogeneration system, optimal control can add up to 67% to the value of the cogeneration system; optimal control adds less value in locations where cogeneration is more clearly profitable; (2) optimal control under real-time pricing is (a) more complicated than under typical time-of-use tariffs and (b) at times necessary to make cogeneration economic at all; (3) limited electric load curtailment opportunities can be more valuable as a compliment to the cogeneration system than alone; and (4) most of the trade-off between least-cost and least-carbon IES is determined during the system design stage; for the IES system considered, there is little difference between least-cost control and least-carbon control.« less

  3. Optimal symmetric flight studies

    NASA Technical Reports Server (NTRS)

    Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.

    1985-01-01

    Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.

  4. Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)

    NASA Astrophysics Data System (ADS)

    Harmening, Corinna; Neuner, Hans

    2016-09-01

    Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.

  5. A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems.

    PubMed

    Padhi, Radhakant; Unnikrishnan, Nishant; Wang, Xiaohua; Balakrishnan, S N

    2006-12-01

    Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the "Single Network Adaptive Critic (SNAC)" is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

  6. Universal approximators for multi-objective direct policy search in water reservoir management problems: a comparative analysis

    NASA Astrophysics Data System (ADS)

    Giuliani, Matteo; Mason, Emanuele; Castelletti, Andrea; Pianosi, Francesca

    2014-05-01

    The optimal operation of water resources systems is a wide and challenging problem due to non-linearities in the model and the objectives, high dimensional state-control space, and strong uncertainties in the hydroclimatic regimes. The application of classical optimization techniques (e.g., SDP, Q-learning, gradient descent-based algorithms) is strongly limited by the dimensionality of the system and by the presence of multiple, conflicting objectives. This study presents a novel approach which combines Direct Policy Search (DPS) and Multi-Objective Evolutionary Algorithms (MOEAs) to solve high-dimensional state and control space problems involving multiple objectives. DPS, also known as parameterization-simulation-optimization in the water resources literature, is a simulation-based approach where the reservoir operating policy is first parameterized within a given family of functions and, then, the parameters optimized with respect to the objectives of the management problem. The selection of a suitable class of functions to which the operating policy belong to is a key step, as it might restrict the search for the optimal policy to a subspace of the decision space that does not include the optimal solution. In the water reservoir literature, a number of classes have been proposed. However, many of these rules are based largely on empirical or experimental successes and they were designed mostly via simulation and for single-purpose reservoirs. In a multi-objective context similar rules can not easily inferred from the experience and the use of universal function approximators is generally preferred. In this work, we comparatively analyze two among the most common universal approximators: artificial neural networks (ANN) and radial basis functions (RBF) under different problem settings to estimate their scalability and flexibility in dealing with more and more complex problems. The multi-purpose HoaBinh water reservoir in Vietnam, accounting for hydropower production and flood control, is used as a case study. Preliminary results show that the RBF policy parametrization is more effective than the ANN one. In particular, the approximated Pareto front obtained with RBF control policies successfully explores the full tradeoff space between the two conflicting objectives, while most of the ANN solutions results to be Pareto-dominated by the RBF ones.

  7. Optimal causal inference: estimating stored information and approximating causal architecture.

    PubMed

    Still, Susanne; Crutchfield, James P; Ellison, Christopher J

    2010-09-01

    We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate-distortion theory to use causal shielding--a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that in the limit in which a model-complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of the underlying causal states can be found by optimal causal estimation. A previously derived model-complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid overfitting.

  8. Near-Optimal Tracking Control of Mobile Robots Via Receding-Horizon Dual Heuristic Programming.

    PubMed

    Lian, Chuanqiang; Xu, Xin; Chen, Hong; He, Haibo

    2016-11-01

    Trajectory tracking control of wheeled mobile robots (WMRs) has been an important research topic in control theory and robotics. Although various tracking control methods with stability have been developed for WMRs, it is still difficult to design optimal or near-optimal tracking controller under uncertainties and disturbances. In this paper, a near-optimal tracking control method is presented for WMRs based on receding-horizon dual heuristic programming (RHDHP). In the proposed method, a backstepping kinematic controller is designed to generate desired velocity profiles and the receding horizon strategy is used to decompose the infinite-horizon optimal control problem into a series of finite-horizon optimal control problems. In each horizon, a closed-loop tracking control policy is successively updated using a class of approximate dynamic programming algorithms called finite-horizon dual heuristic programming (DHP). The convergence property of the proposed method is analyzed and it is shown that the tracking control system based on RHDHP is asymptotically stable by using the Lyapunov approach. Simulation results on three tracking control problems demonstrate that the proposed method has improved control performance when compared with conventional model predictive control (MPC) and DHP. It is also illustrated that the proposed method has lower computational burden than conventional MPC, which is very beneficial for real-time tracking control.

  9. Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance Using ADP.

    PubMed

    Wei, Qinglai; Song, Ruizhuo; Yan, Pengfei

    2016-02-01

    This paper is concerned with a new data-driven zero-sum neuro-optimal control problem for continuous-time unknown nonlinear systems with disturbance. According to the input-output data of the nonlinear system, an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system. Considering the system disturbance as a control input, a two-player zero-sum optimal control problem is established. Adaptive dynamic programming (ADP) is developed to obtain the optimal control under the worst case of the disturbance. Three single-layer neural networks, including one critic and two action networks, are employed to approximate the performance index function, the optimal control law, and the disturbance, respectively, for facilitating the implementation of the ADP method. Convergence properties of the ADP method are developed to show that the system state will converge to a finite neighborhood of the equilibrium. The weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones. Finally, the simulation results will show the effectiveness of the developed data-driven ADP methods.

  10. Optimal control of parametric oscillations of compressed flexible bars

    NASA Astrophysics Data System (ADS)

    Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

    2018-05-01

    In this paper the problem of damping of the linear systems oscillations with piece-wise constant control is solved. The motion of bar construction is reduced to the form described by Hill's differential equation using the Bubnov-Galerkin method. To calculate switching moments of the one-side control the method of sequential linear programming is used. The elements of the fundamental matrix of the Hill's equation are approximated by trigonometric series. Examples of the optimal control of the systems for various initial conditions and different number of control stages have been calculated. The corresponding phase trajectories and transient processes are represented.

  11. On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.

    2011-01-01

    This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

  12. Neural networks for feedback feedforward nonlinear control systems.

    PubMed

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

  13. Full-order optimal compensators for flow control: the multiple inputs case

    NASA Astrophysics Data System (ADS)

    Semeraro, Onofrio; Pralits, Jan O.

    2018-03-01

    Flow control has been the subject of numerous experimental and theoretical works. We analyze full-order, optimal controllers for large dynamical systems in the presence of multiple actuators and sensors. The full-order controllers do not require any preliminary model reduction or low-order approximation: this feature allows us to assess the optimal performance of an actuated flow without relying on any estimation process or further hypothesis on the disturbances. We start from the original technique proposed by Bewley et al. (Meccanica 51(12):2997-3014, 2016. https://doi.org/10.1007/s11012-016-0547-3), the adjoint of the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows bypassing the solution of the algebraic Riccati equation associated with the optimal control problem, typically infeasible for large systems. In this numerical work, we extend the ADA iteration into a more general framework that includes the design of controllers with multiple, coupled inputs and robust controllers (H_{∞} methods). First, we demonstrate our results by showing the analytical equivalence between the full Riccati solutions and the ADA approximations in the multiple inputs case. In the second part of the article, we analyze the performance of the algorithm in terms of convergence of the solution, by comparing it with analogous techniques. We find an excellent scalability with the number of inputs (actuators), making the method a viable way for full-order control design in complex settings. Finally, the applicability of the algorithm to fluid mechanics problems is shown using the linearized Kuramoto-Sivashinsky equation and the Kármán vortex street past a two-dimensional cylinder.

  14. Guidance and Control strategies for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

    1989-01-01

    A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

  15. Transient analysis of an adaptive system for optimization of design parameters

    NASA Technical Reports Server (NTRS)

    Bayard, D. S.

    1992-01-01

    Averaging methods are applied to analyzing and optimizing the transient response associated with the direct adaptive control of an oscillatory second-order minimum-phase system. The analytical design methods developed for a second-order plant can be applied with some approximation to a MIMO flexible structure having a single dominant mode.

  16. Adaptive effort investment in cognitive and physical tasks: a neurocomputational model

    PubMed Central

    Verguts, Tom; Vassena, Eliana; Silvetti, Massimo

    2015-01-01

    Despite its importance in everyday life, the computational nature of effort investment remains poorly understood. We propose an effort model obtained from optimality considerations, and a neurocomputational approximation to the optimal model. Both are couched in the framework of reinforcement learning. It is shown that choosing when or when not to exert effort can be adaptively learned, depending on rewards, costs, and task difficulty. In the neurocomputational model, the limbic loop comprising anterior cingulate cortex (ACC) and ventral striatum in the basal ganglia allocates effort to cortical stimulus-action pathways whenever this is valuable. We demonstrate that the model approximates optimality. Next, we consider two hallmark effects from the cognitive control literature, namely proportion congruency and sequential congruency effects. It is shown that the model exerts both proactive and reactive cognitive control. Then, we simulate two physical effort tasks. In line with empirical work, impairing the model's dopaminergic pathway leads to apathetic behavior. Thus, we conceptually unify the exertion of cognitive and physical effort, studied across a variety of literatures (e.g., motivation and cognitive control) and animal species. PMID:25805978

  17. Genetic Algorithm Optimizes Q-LAW Control Parameters

    NASA Technical Reports Server (NTRS)

    Lee, Seungwon; von Allmen, Paul; Petropoulos, Anastassios; Terrile, Richard

    2008-01-01

    A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.

  18. Approximation algorithms for planning and control

    NASA Technical Reports Server (NTRS)

    Boddy, Mark; Dean, Thomas

    1989-01-01

    A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.

  19. Development of an hp-version finite element method for computational optimal control

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Warner, Michael S.

    1993-01-01

    The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.

  20. Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

    PubMed

    Luo, Biao; Liu, Derong; Wu, Huai-Ning

    2018-06-01

    Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

  1. Stochastic Optimal Control via Bellman's Principle

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Sun, Jian Q.

    2003-01-01

    This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

  2. Optimal placement of actuators and sensors in control augmented structural optimization

    NASA Technical Reports Server (NTRS)

    Sepulveda, A. E.; Schmit, L. A., Jr.

    1990-01-01

    A control-augmented structural synthesis methodology is presented in which actuator and sensor placement is treated in terms of (0,1) variables. Structural member sizes and control variables are treated simultaneously as design variables. A multiobjective utopian approach is used to obtain a compromise solution for inherently conflicting objective functions such as strucutal mass control effort and number of actuators. Constraints are imposed on transient displacements, natural frequencies, actuator forces and dynamic stability as well as controllability and observability of the system. The combinatorial aspects of the mixed - (0,1) continuous variable design optimization problem are made tractable by combining approximation concepts with branch and bound techniques. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.

  3. Optimal control of a variable spin speed CMG system for space vehicles. [Control Moment Gyros

    NASA Technical Reports Server (NTRS)

    Liu, T. C.; Chubb, W. B.; Seltzer, S. M.; Thompson, Z.

    1973-01-01

    Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

  4. Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

    PubMed

    Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

    2018-05-01

    In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.

  5. Multigrid one shot methods for optimal control problems: Infinite dimensional control

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Taasan, Shlomo

    1994-01-01

    The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

  6. Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

    NASA Technical Reports Server (NTRS)

    Kenny, Sean P.; Hou, Gene J. W.

    1994-01-01

    A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

  7. Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems.

    PubMed

    Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan

    2015-01-01

    Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

  8. Towards sub-optimal stochastic control of partially observable stochastic systems

    NASA Technical Reports Server (NTRS)

    Ruzicka, G. J.

    1980-01-01

    A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

  9. Stabilization of model-based networked control systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Miranda, Francisco; Instituto Politécnico de Viana do Castelo, Viana do Castelo; Abreu, Carlos

    2016-06-08

    A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtainmore » an optimal feedback control is also presented.« less

  10. Optimal solutions for a bio mathematical model for the evolution of smoking habit

    NASA Astrophysics Data System (ADS)

    Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

    In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

  11. Control system estimation and design for aerospace vehicles with time delay

    NASA Technical Reports Server (NTRS)

    Allgaier, G. R.; Williams, T. L.

    1972-01-01

    The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

  12. Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

    NASA Astrophysics Data System (ADS)

    Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

    2017-08-01

    The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

  13. Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

    PubMed

    Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

    2018-06-01

    This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

  14. Interception in three dimensions - An energy formulation

    NASA Technical Reports Server (NTRS)

    Rajan, N.; Ardema, M. D.

    1983-01-01

    The problem of minimum-time interception of a target flying in three dimensional space is analyzed with the interceptor aircraft modeled through energy-state approximation. A coordinate transformation that uncouples the interceptor's extremals from the target motion in an open-loop sense is introduced, and the necessary conditions for optimality and the optimal controls are derived. Example extremals are shown.

  15. Autonomous vehicle motion control, approximate maps, and fuzzy logic

    NASA Technical Reports Server (NTRS)

    Ruspini, Enrique H.

    1993-01-01

    Progress on research on the control of actions of autonomous mobile agents using fuzzy logic is presented. The innovations described encompass theoretical and applied developments. At the theoretical level, results of research leading to the combined utilization of conventional artificial planning techniques with fuzzy logic approaches for the control of local motion and perception actions are presented. Also formulations of dynamic programming approaches to optimal control in the context of the analysis of approximate models of the real world are examined. Also a new approach to goal conflict resolution that does not require specification of numerical values representing relative goal importance is reviewed. Applied developments include the introduction of the notion of approximate map. A fuzzy relational database structure for the representation of vague and imprecise information about the robot's environment is proposed. Also the central notions of control point and control structure are discussed.

  16. Advanced rotorcraft control using parameter optimization

    NASA Technical Reports Server (NTRS)

    Vansteenwyk, Brett; Ly, Uy-Loi

    1991-01-01

    A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

  17. Simulation and optimal control of wind-farm boundary layers

    NASA Astrophysics Data System (ADS)

    Meyers, Johan; Goit, Jay

    2014-05-01

    In large wind farms, the effect of turbine wakes, and their interaction leads to a reduction in farm efficiency, with power generated by turbines in a farm being lower than that of a lone-standing turbine by up to 50%. In very large wind farms or `deep arrays', this efficiency loss is related to interaction of the wind farms with the planetary boundary layer, leading to lower wind speeds at turbine level. Moreover, for these cases it has been demonstrated both in simulations and wind-tunnel experiments that the wind-farm energy extraction is dominated by the vertical turbulent transport of kinetic energy from higher regions in the boundary layer towards the turbine level. In the current study, we investigate the use of optimal control techniques combined with Large-Eddy Simulations (LES) of wind-farm boundary layer interaction for the increase of total energy extraction in very large `infinite' wind farms. We consider the individual wind turbines as flow actuators, whose energy extraction can be dynamically regulated in time so as to optimally influence the turbulent flow field, maximizing the wind farm power. For the simulation of wind-farm boundary layers we use large-eddy simulations in combination with actuator-disk and actuator-line representations of wind turbines. Simulations are performed in our in-house pseudo-spectral code SP-Wind that combines Fourier-spectral discretization in horizontal directions with a fourth-order finite-volume approach in the vertical direction. For the optimal control study, we consider the dynamic control of turbine-thrust coefficients in an actuator-disk model. They represent the effect of turbine blades that can actively pitch in time, changing the lift- and drag coefficients of the turbine blades. Optimal model-predictive control (or optimal receding horizon control) is used, where the model simply consists of the full LES equations, and the time horizon is approximately 280 seconds. The optimization is performed using a nonlinear conjugate gradient method, and the gradients are calculated by solving the adjoint LES equations. We find that the extracted farm power increases by approximately 20% when using optimal model-predictive control. However, the increased power output is also responsible for an increase in turbulent dissipation, and a deceleration of the boundary layer. Further investigating the energy balances in the boundary layer, it is observed that this deceleration is mainly occurring in the outer layer as a result of higher turbulent energy fluxes towards the turbines. In a second optimization case, we penalize boundary-layer deceleration, and find an increase of energy extraction of approximately 10%. In this case, increased energy extraction is balanced by a reduction in of turbulent dissipation in the boundary layer. J.M. acknowledges support from the European Research Council (FP7-Ideas, grant no. 306471). Simulations were performed on the computing infrastructure of the VSC Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government.

  18. Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

    PubMed

    Wei, Qinglai; Liu, Derong; Lin, Qiao

    In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

  19. Optimal Control-Based Adaptive NN Design for a Class of Nonlinear Discrete-Time Block-Triangular Systems.

    PubMed

    Liu, Yan-Jun; Tong, Shaocheng

    2016-11-01

    In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.

  20. Chandrasekhar equations and computational algorithms for distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Burns, J. A.; Ito, K.; Powers, R. K.

    1984-01-01

    The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

  1. Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

    NASA Technical Reports Server (NTRS)

    Tiffany, Sherwood H.; Karpel, Mordechay

    1989-01-01

    Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

  2. Reliable numerical computation in an optimal output-feedback design

    NASA Technical Reports Server (NTRS)

    Vansteenwyk, Brett; Ly, Uy-Loi

    1991-01-01

    A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

  3. Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes

    NASA Astrophysics Data System (ADS)

    Jäger, Georg; Reich, Daniel M.; Goerz, Michael H.; Koch, Christiane P.; Hohenester, Ulrich

    2014-09-01

    We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation, and to excite a condensate from the ground state to the first-excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use; namely, gradient-ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second-order-derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step-size parameter converges faster but can produce sharp features in the control fields.

  4. Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

    NASA Technical Reports Server (NTRS)

    Pinson, Robin; Lu, Ping

    2015-01-01

    This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

  5. Improved control of medical x-ray film exposure

    NASA Technical Reports Server (NTRS)

    Berdahl, C. M.

    1978-01-01

    Exposure sensing system for light-intensified motion-picture X-ray system uses aperture or adjustable diaphragm to sample light from image region of interest. Approach, along with approximate optics, can optimize exposure sensitivity.

  6. Energy management of three-dimensional minimum-time intercept. [for aircraft flight optimization

    NASA Technical Reports Server (NTRS)

    Kelley, H. J.; Cliff, E. M.; Visser, H. G.

    1985-01-01

    A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

  7. Using block pulse functions for seismic vibration semi-active control of structures with MR dampers

    NASA Astrophysics Data System (ADS)

    Rahimi Gendeshmin, Saeed; Davarnia, Daniel

    2018-03-01

    This article applied the idea of block pulse functions in the semi-active control of structures. The BP functions give effective tools to approximate complex problems. The applied control algorithm has a major effect on the performance of the controlled system and the requirements of the control devices. In control problems, it is important to devise an accurate analytical technique with less computational cost. It is proved that the BP functions are fundamental tools in approximation problems which have been applied in disparate areas in last decades. This study focuses on the employment of BP functions in control algorithm concerning reduction the computational cost. Magneto-rheological (MR) dampers are one of the well-known semi-active tools that can be used to control the response of civil Structures during earthquake. For validation purposes, numerical simulations of a 5-story shear building frame with MR dampers are presented. The results of suggested method were compared with results obtained by controlling the frame by the optimal control method based on linear quadratic regulator theory. It can be seen from simulation results that the suggested method can be helpful in reducing seismic structural responses. Besides, this method has acceptable accuracy and is in agreement with optimal control method with less computational costs.

  8. Fast engineering optimization: A novel highly effective control parameterization approach for industrial dynamic processes.

    PubMed

    Liu, Ping; Li, Guodong; Liu, Xinggao

    2015-09-01

    Control vector parameterization (CVP) is an important approach of the engineering optimization for the industrial dynamic processes. However, its major defect, the low optimization efficiency caused by calculating the relevant differential equations in the generated nonlinear programming (NLP) problem repeatedly, limits its wide application in the engineering optimization for the industrial dynamic processes. A novel highly effective control parameterization approach, fast-CVP, is first proposed to improve the optimization efficiency for industrial dynamic processes, where the costate gradient formulae is employed and a fast approximate scheme is presented to solve the differential equations in dynamic process simulation. Three well-known engineering optimization benchmark problems of the industrial dynamic processes are demonstrated as illustration. The research results show that the proposed fast approach achieves a fine performance that at least 90% of the computation time can be saved in contrast to the traditional CVP method, which reveals the effectiveness of the proposed fast engineering optimization approach for the industrial dynamic processes. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  9. The control of a parallel hybrid-electric propulsion system for a small unmanned aerial vehicle using a CMAC neural network.

    PubMed

    Harmon, Frederick G; Frank, Andrew A; Joshi, Sanjay S

    2005-01-01

    A Simulink model, a propulsion energy optimization algorithm, and a CMAC controller were developed for a small parallel hybrid-electric unmanned aerial vehicle (UAV). The hybrid-electric UAV is intended for military, homeland security, and disaster-monitoring missions involving intelligence, surveillance, and reconnaissance (ISR). The Simulink model is a forward-facing simulation program used to test different control strategies. The flexible energy optimization algorithm for the propulsion system allows relative importance to be assigned between the use of gasoline, electricity, and recharging. A cerebellar model arithmetic computer (CMAC) neural network approximates the energy optimization results and is used to control the parallel hybrid-electric propulsion system. The hybrid-electric UAV with the CMAC controller uses 67.3% less energy than a two-stroke gasoline-powered UAV during a 1-h ISR mission and 37.8% less energy during a longer 3-h ISR mission.

  10. Thermal/structural Tailoring of Engine Blades (T/SEAEBL). Theoretical Manual

    NASA Technical Reports Server (NTRS)

    Brown, K. W.; Clevenger, W. B.

    1994-01-01

    The Thermal/Structural Tailoring of Engine Blades (T/STAEBL) system is a family of computer programs executed by a control program. The T/STAEBL system performs design optimizations of cooled, hollow turbine blades and vanes. This manual describes the T/STAEBL data block structure and system organization. The approximate analysis and optimization modules are detailed, and a validation test case is provided.

  11. Thermal/structural tailoring of engine blades (T/SEAEBL). Theoretical manual

    NASA Astrophysics Data System (ADS)

    Brown, K. W.; Clevenger, W. B.

    1994-03-01

    The Thermal/Structural Tailoring of Engine Blades (T/STAEBL) system is a family of computer programs executed by a control program. The T/STAEBL system performs design optimizations of cooled, hollow turbine blades and vanes. This manual describes the T/STAEBL data block structure and system organization. The approximate analysis and optimization modules are detailed, and a validation test case is provided.

  12. Approximate Linear Regulator and Kalman Filter

    DTIC Science & Technology

    1980-09-01

    of Equivalent Dominant Poles and Zeros Using Industrial Specifications," IEEE Trans. on Industrial Electronics and Control Instrumentation, Vol. IECI...true. In recent years, the rapid development of powerful minicomputers and microprocessors makes the industrial applications of optimal control...1976, pp. 677-687. [21] Y. Takahashi, M. Tomizuka and D. I. Auslander, Simple discrete control of industrial processes, Trans. on ASME J. of Dynamic

  13. Bounded-Degree Approximations of Stochastic Networks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

    2017-06-01

    We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less

  14. Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.

    PubMed

    Fan, Quan-Yong; Yang, Guang-Hong

    2016-01-01

    This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.

  15. A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.

    2004-01-01

    The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

  16. ORACLS: A system for linear-quadratic-Gaussian control law design

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  17. Self-optimization and auto-stabilization of receiver in DPSK transmission system.

    PubMed

    Jang, Y S

    2008-03-17

    We propose a self-optimization and auto-stabilization method for a 1-bit DMZI in DPSK transmission. Using the characteristics of eye patterns, the optical frequency transmittance of a 1-bit DMZI is thermally controlled to maximize the power difference between the constructive and destructive output ports. Unlike other techniques, this control method can be realized without additional components, making it simple and cost effective. Experimental results show that error-free performance is maintained when the carrier optical frequency variation is approximately 10% of the data rate.

  18. Obtaining Approximate Values of Exterior Orientation Elements of Multi-Intersection Images Using Particle Swarm Optimization

    NASA Astrophysics Data System (ADS)

    Li, X.; Li, S. W.

    2012-07-01

    In this paper, an efficient global optimization algorithm in the field of artificial intelligence, named Particle Swarm Optimization (PSO), is introduced into close range photogrammetric data processing. PSO can be applied to obtain the approximate values of exterior orientation elements under the condition that multi-intersection photography and a small portable plane control frame are used. PSO, put forward by an American social psychologist J. Kennedy and an electrical engineer R.C. Eberhart, is a stochastic global optimization method based on swarm intelligence, which was inspired by social behavior of bird flocking or fish schooling. The strategy of obtaining the approximate values of exterior orientation elements using PSO is as follows: in terms of image coordinate observed values and space coordinates of few control points, the equations of calculating the image coordinate residual errors can be given. The sum of absolute value of each image coordinate is minimized to be the objective function. The difference between image coordinate observed value and the image coordinate computed through collinear condition equation is defined as the image coordinate residual error. Firstly a gross area of exterior orientation elements is given, and then the adjustment of other parameters is made to get the particles fly in the gross area. After iterative computation for certain times, the satisfied approximate values of exterior orientation elements are obtained. By doing so, the procedures like positioning and measuring space control points in close range photogrammetry can be avoided. Obviously, this method can improve the surveying efficiency greatly and at the same time can decrease the surveying cost. And during such a process, only one small portable control frame with a couple of control points is employed, and there are no strict requirements for the space distribution of control points. In order to verify the effectiveness of this algorithm, two experiments are carried out. In the first experiment, images of a standard grid board are taken according to multi-intersection photography using digital camera. Three points or six points which are located on the left-down corner of the standard grid are regarded as control points respectively, and the exterior orientation elements of each image are computed through PSO, and compared with these elements computed through bundle adjustment. In the second experiment, the exterior orientation elements obtained from the first experiment are used as approximate values in bundle adjustment and then the space coordinates of other grid points on the board can be computed. The coordinate difference of grid points between these computed space coordinates and their known coordinates can be used to compute the accuracy. The point accuracy computed in above experiments are ±0.76mm and ±0.43mm respectively. The above experiments prove the effectiveness of PSO used in close range photogrammetry to compute approximate values of exterior orientation elements, and the algorithm can meet the requirement of higher accuracy. In short, PSO can get better results in a faster, cheaper way compared with other surveying methods in close range photogrammetry.

  19. Personality traits associated with genetic counselor compassion fatigue: the roles of dispositional optimism and locus of control.

    PubMed

    Injeyan, Marie C; Shuman, Cheryl; Shugar, Andrea; Chitayat, David; Atenafu, Eshetu G; Kaiser, Amy

    2011-10-01

    Compassion fatigue (CMF) arises as a consequence of secondary exposure to distress and can be elevated in some health practitioners. Locus of control and dispositional optimism are aspects of personality known to influence coping style. To investigate whether these personality traits influence CMF risk, we surveyed 355 genetic counselors about their CMF, locus of control orientation, and degree of dispositional optimism. Approximately half of respondents reported they experience CMF; 26.6% had considered leaving their job due to CMF symptoms. Mixed-method analyses revealed that genetic counselors having an external locus of control and low optimism were at highest risk for CMF. Those at highest risk experienced moderate-to-high burnout, low-to-moderate compassion satisfaction, and tended to rely on religion/spirituality when coping with stress. CMF risk was not influenced by years in practice, number of genetic counselor colleagues in the workplace, or completion of graduate training in this area. Recommendations for practice and education are outlined.

  20. Optimal landing of a helicopter in autorotation

    NASA Technical Reports Server (NTRS)

    Lee, A. Y. N.

    1985-01-01

    Gliding descent in autorotation is a maneuver used by helicopter pilots in case of engine failure. The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. The OH-58A helicopter was used. Helicopter vertical and horizontal velocities, vertical and horizontal displacement, and the rotor angle speed were modeled. An empirical approximation for the induced veloctiy in the vortex-ring state were provided. The cost function of the optimal control problem is a weighted sum of the squared horizontal and vertical components of the helicopter velocity at touchdown. Optimal trajectories are calculated for entry conditions well within the horizontal-vertical restriction curve, with the helicopter initially in hover or forwared flight. The resultant two-point boundary value problem with path equality constraints was successfully solved using the Sequential Gradient Restoration Technique.

  1. Trajectory optimization for the National Aerospace Plane

    NASA Technical Reports Server (NTRS)

    Lu, Ping

    1993-01-01

    The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

  2. Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

    This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less

  3. A Routing Protocol for Multisink Wireless Sensor Networks in Underground Coalmine Tunnels

    PubMed Central

    Xia, Xu; Chen, Zhigang; Liu, Hui; Wang, Huihui; Zeng, Feng

    2016-01-01

    Traditional underground coalmine monitoring systems are mainly based on the use of wired transmission. However, when cables are damaged during an accident, it is difficult to obtain relevant data on environmental parameters and the emergency situation underground. To address this problem, the use of wireless sensor networks (WSNs) has been proposed. However, the shape of coalmine tunnels is not conducive to the deployment of WSNs as they are long and narrow. Therefore, issues with the network arise, such as extremely large energy consumption, very weak connectivity, long time delays, and a short lifetime. To solve these problems, in this study, a new routing protocol algorithm for multisink WSNs based on transmission power control is proposed. First, a transmission power control algorithm is used to negotiate the optimal communication radius and transmission power of each sink. Second, the non-uniform clustering idea is adopted to optimize the cluster head selection. Simulation results are subsequently compared to the Centroid of the Nodes in a Partition (CNP) strategy and show that the new algorithm delivers a good performance: power efficiency is increased by approximately 70%, connectivity is increased by approximately 15%, the cluster interference is diminished by approximately 50%, the network lifetime is increased by approximately 6%, and the delay is reduced with an increase in the number of sinks. PMID:27916917

  4. A Routing Protocol for Multisink Wireless Sensor Networks in Underground Coalmine Tunnels.

    PubMed

    Xia, Xu; Chen, Zhigang; Liu, Hui; Wang, Huihui; Zeng, Feng

    2016-11-30

    Traditional underground coalmine monitoring systems are mainly based on the use of wired transmission. However, when cables are damaged during an accident, it is difficult to obtain relevant data on environmental parameters and the emergency situation underground. To address this problem, the use of wireless sensor networks (WSNs) has been proposed. However, the shape of coalmine tunnels is not conducive to the deployment of WSNs as they are long and narrow. Therefore, issues with the network arise, such as extremely large energy consumption, very weak connectivity, long time delays, and a short lifetime. To solve these problems, in this study, a new routing protocol algorithm for multisink WSNs based on transmission power control is proposed. First, a transmission power control algorithm is used to negotiate the optimal communication radius and transmission power of each sink. Second, the non-uniform clustering idea is adopted to optimize the cluster head selection. Simulation results are subsequently compared to the Centroid of the Nodes in a Partition (CNP) strategy and show that the new algorithm delivers a good performance: power efficiency is increased by approximately 70%, connectivity is increased by approximately 15%, the cluster interference is diminished by approximately 50%, the network lifetime is increased by approximately 6%, and the delay is reduced with an increase in the number of sinks.

  5. Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

    NASA Astrophysics Data System (ADS)

    Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

    2016-03-01

    Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

  6. Building Energy Modeling and Control Methods for Optimization and Renewables Integration

    NASA Astrophysics Data System (ADS)

    Burger, Eric M.

    This dissertation presents techniques for the numerical modeling and control of building systems, with an emphasis on thermostatically controlled loads. The primary objective of this work is to address technical challenges related to the management of energy use in commercial and residential buildings. This work is motivated by the need to enhance the performance of building systems and by the potential for aggregated loads to perform load following and regulation ancillary services, thereby enabling the further adoption of intermittent renewable energy generation technologies. To increase the generalizability of the techniques, an emphasis is placed on recursive and adaptive methods which minimize the need for customization to specific buildings and applications. The techniques presented in this dissertation can be divided into two general categories: modeling and control. Modeling techniques encompass the processing of data streams from sensors and the training of numerical models. These models enable us to predict the energy use of a building and of sub-systems, such as a heating, ventilation, and air conditioning (HVAC) unit. Specifically, we first present an ensemble learning method for the short-term forecasting of total electricity demand in buildings. As the deployment of intermittent renewable energy resources continues to rise, the generation of accurate building-level electricity demand forecasts will be valuable to both grid operators and building energy management systems. Second, we present a recursive parameter estimation technique for identifying a thermostatically controlled load (TCL) model that is non-linear in the parameters. For TCLs to perform demand response services in real-time markets, online methods for parameter estimation are needed. Third, we develop a piecewise linear thermal model of a residential building and train the model using data collected from a custom-built thermostat. This model is capable of approximating unmodeled dynamics within a building by learning from sensor data. Control techniques encompass the application of optimal control theory, model predictive control, and convex distributed optimization to TCLs. First, we present the alternative control trajectory (ACT) representation, a novel method for the approximate optimization of non-convex discrete systems. This approach enables the optimal control of a population of non-convex agents using distributed convex optimization techniques. Second, we present a distributed convex optimization algorithm for the control of a TCL population. Experimental results demonstrate the application of this algorithm to the problem of renewable energy generation following. This dissertation contributes to the development of intelligent energy management systems for buildings by presenting a suite of novel and adaptable modeling and control techniques. Applications focus on optimizing the performance of building operations and on facilitating the integration of renewable energy resources.

  7. Reliability-Based Control Design for Uncertain Systems

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Kenny, Sean P.

    2005-01-01

    This paper presents a robust control design methodology for systems with probabilistic parametric uncertainty. Control design is carried out by solving a reliability-based multi-objective optimization problem where the probability of violating design requirements is minimized. Simultaneously, failure domains are optimally enlarged to enable global improvements in the closed-loop performance. To enable an efficient numerical implementation, a hybrid approach for estimating reliability metrics is developed. This approach, which integrates deterministic sampling and asymptotic approximations, greatly reduces the numerical burden associated with complex probabilistic computations without compromising the accuracy of the results. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

  8. Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

  9. Helicopter Control Energy Reduction Using Moving Horizontal Tail

    PubMed Central

    Oktay, Tugrul; Sal, Firat

    2015-01-01

    Helicopter moving horizontal tail (i.e., MHT) strategy is applied in order to save helicopter flight control system (i.e., FCS) energy. For this intention complex, physics-based, control-oriented nonlinear helicopter models are used. Equations of MHT are integrated into these models and they are together linearized around straight level flight condition. A specific variance constrained control strategy, namely, output variance constrained Control (i.e., OVC) is utilized for helicopter FCS. Control energy savings due to this MHT idea with respect to a conventional helicopter are calculated. Parameters of helicopter FCS and dimensions of MHT are simultaneously optimized using a stochastic optimization method, namely, simultaneous perturbation stochastic approximation (i.e., SPSA). In order to observe improvement in behaviors of classical controls closed loop analyses are done. PMID:26180841

  10. CO 2 water-alternating-gas injection for enhanced oil recovery: Optimal well controls and half-cycle lengths

    DOE PAGES

    Chen, Bailian; Reynolds, Albert C.

    2018-03-11

    We report that CO 2 water-alternating-gas (WAG) injection is an enhanced oil recovery method designed to improve sweep efficiency during CO 2 injection with the injected water to control the mobility of CO 2 and to stabilize the gas front. Optimization of CO 2 -WAG injection is widely regarded as a viable technique for controlling the CO 2 and oil miscible process. Poor recovery from CO 2 -WAG injection can be caused by inappropriately designed WAG parameters. In previous study (Chen and Reynolds, 2016), we proposed an algorithm to optimize the well controls which maximize the life-cycle net-present-value (NPV). However,more » the effect of injection half-cycle lengths for each injector on oil recovery or NPV has not been well investigated. In this paper, an optimization framework based on augmented Lagrangian method and the newly developed stochastic-simplex-approximate-gradient (StoSAG) algorithm is proposed to explore the possibility of simultaneous optimization of the WAG half-cycle lengths together with the well controls. Finally, the proposed framework is demonstrated with three reservoir examples.« less

  11. CO 2 water-alternating-gas injection for enhanced oil recovery: Optimal well controls and half-cycle lengths

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Bailian; Reynolds, Albert C.

    We report that CO 2 water-alternating-gas (WAG) injection is an enhanced oil recovery method designed to improve sweep efficiency during CO 2 injection with the injected water to control the mobility of CO 2 and to stabilize the gas front. Optimization of CO 2 -WAG injection is widely regarded as a viable technique for controlling the CO 2 and oil miscible process. Poor recovery from CO 2 -WAG injection can be caused by inappropriately designed WAG parameters. In previous study (Chen and Reynolds, 2016), we proposed an algorithm to optimize the well controls which maximize the life-cycle net-present-value (NPV). However,more » the effect of injection half-cycle lengths for each injector on oil recovery or NPV has not been well investigated. In this paper, an optimization framework based on augmented Lagrangian method and the newly developed stochastic-simplex-approximate-gradient (StoSAG) algorithm is proposed to explore the possibility of simultaneous optimization of the WAG half-cycle lengths together with the well controls. Finally, the proposed framework is demonstrated with three reservoir examples.« less

  12. Wide-area Power System Damping Control Coordination Based on Particle Swarm Optimization with Time Delay Considered

    NASA Astrophysics Data System (ADS)

    Zhang, J. Y.; Jiang, Y.

    2017-10-01

    To ensure satisfactory dynamic performance of controllers in time-delayed power systems, a WAMS-based control strategy is investigated in the presence of output feedback delay. An integrated approach based on Pade approximation and particle swarm optimization (PSO) is employed for parameter configuration of PSS. The coordination configuration scheme of power system controllers is achieved by a series of stability constraints at the aim of maximizing the minimum damping ratio of inter-area mode of power system. The validity of this derived PSS is verified on a prototype power system. The findings demonstrate that the proposed approach for control design could damp the inter-area oscillation and enhance the small-signal stability.

  13. Aerodynamic design and optimization in one shot

    NASA Technical Reports Server (NTRS)

    Ta'asan, Shlomo; Kuruvila, G.; Salas, M. D.

    1992-01-01

    This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

  14. L^1 -optimality conditions for the circular restricted three-body problem

    NASA Astrophysics Data System (ADS)

    Chen, Zheng

    2016-11-01

    In this paper, the L^1 -minimization for the translational motion of a spacecraft in the circular restricted three-body problem (CRTBP) is considered. Necessary conditions are derived by using the Pontryagin Maximum Principle (PMP), revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, recalling the existence of the Fuller phenomenon according to the theories developed in (Marchal in J Optim Theory Appl 11(5):441-486, 1973; Zelikin and Borisov in Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering. Birkhäuser, Basal 1994; in J Math Sci 114(3):1227-1344, 2003). The sufficient optimality conditions for the L^1 -minimization problem with fixed endpoints have been developed in (Chen et al. in SIAM J Control Optim 54(3):1245-1265, 2016). In the current paper, we establish second-order conditions for optimal control problems with more general final conditions defined by a smooth submanifold target. In addition, the numerical implementation to check these optimality conditions is given. Finally, approximating the Earth-Moon-Spacecraft system by the CRTBP, an L^1 -minimization trajectory for the translational motion of a spacecraft is computed by combining a shooting method with a continuation method in (Caillau et al. in Celest Mech Dyn Astron 114:137-150, 2012; Caillau and Daoud in SIAM J Control Optim 50(6):3178-3202, 2012). The local optimality of the computed trajectory is asserted thanks to the second-order optimality conditions developed.

  15. An efficient hybrid approach for multiobjective optimization of water distribution systems

    NASA Astrophysics Data System (ADS)

    Zheng, Feifei; Simpson, Angus R.; Zecchin, Aaron C.

    2014-05-01

    An efficient hybrid approach for the design of water distribution systems (WDSs) with multiple objectives is described in this paper. The objectives are the minimization of the network cost and maximization of the network resilience. A self-adaptive multiobjective differential evolution (SAMODE) algorithm has been developed, in which control parameters are automatically adapted by means of evolution instead of the presetting of fine-tuned parameter values. In the proposed method, a graph algorithm is first used to decompose a looped WDS into a shortest-distance tree (T) or forest, and chords (Ω). The original two-objective optimization problem is then approximated by a series of single-objective optimization problems of the T to be solved by nonlinear programming (NLP), thereby providing an approximate Pareto optimal front for the original whole network. Finally, the solutions at the approximate front are used to seed the SAMODE algorithm to find an improved front for the original entire network. The proposed approach is compared with two other conventional full-search optimization methods (the SAMODE algorithm and the NSGA-II) that seed the initial population with purely random solutions based on three case studies: a benchmark network and two real-world networks with multiple demand loading cases. Results show that (i) the proposed NLP-SAMODE method consistently generates better-quality Pareto fronts than the full-search methods with significantly improved efficiency; and (ii) the proposed SAMODE algorithm (no parameter tuning) exhibits better performance than the NSGA-II with calibrated parameter values in efficiently offering optimal fronts.

  16. An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

    DTIC Science & Technology

    2012-06-01

    Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

  17. Optimal control of a hybrid rhythmic-discrete task: the bouncing ball revisited.

    PubMed

    Ronsse, Renaud; Wei, Kunlin; Sternad, Dagmar

    2010-05-01

    Rhythmically bouncing a ball with a racket is a hybrid task that combines continuous rhythmic actuation of the racket with the control of discrete impact events between racket and ball. This study presents experimental data and a two-layered modeling framework that explicitly addresses the hybrid nature of control: a first discrete layer calculates the state to reach at impact and the second continuous layer smoothly drives the racket to this desired state, based on optimality principles. The testbed for this hybrid model is task performance at a range of increasingly slower tempos. When slowing the rhythm of the bouncing actions, the continuous cycles become separated into a sequence of discrete movements interspersed by dwell times and directed to achieve the desired impact. Analyses of human performance show increasing variability of performance measures with slower tempi, associated with a change in racket trajectories from approximately sinusoidal to less symmetrical velocity profiles. Matching results of model simulations give support to a hybrid control model based on optimality, and therefore suggest that optimality principles are applicable to the sensorimotor control of complex movements such as ball bouncing.

  18. Downscaling the in vitro test of fungal bioremediation of polycyclic aromatic hydrocarbons: methodological approach.

    PubMed

    Drevinskas, Tomas; Mickienė, Rūta; Maruška, Audrius; Stankevičius, Mantas; Tiso, Nicola; Mikašauskaitė, Jurgita; Ragažinskienė, Ona; Levišauskas, Donatas; Bartkuvienė, Violeta; Snieškienė, Vilija; Stankevičienė, Antanina; Polcaro, Chiara; Galli, Emanuela; Donati, Enrica; Tekorius, Tomas; Kornyšova, Olga; Kaškonienė, Vilma

    2016-02-01

    The miniaturization and optimization of a white rot fungal bioremediation experiment is described in this paper. The optimized procedure allows determination of the degradation kinetics of anthracene. The miniaturized procedure requires only 2.5 ml of culture medium. The experiment is more precise, robust, and better controlled comparing it to classical tests in flasks. Using this technique, different parts, i.e., the culture medium, the fungi, and the cotton seal, can be analyzed. A simple sample preparation speeds up the analytical process. Experiments performed show degradation of anthracene up to approximately 60% by Irpex lacteus and up to approximately 40% by Pleurotus ostreatus in 25 days. Bioremediation of anthracene by the consortium of I. lacteus and P. ostreatus shows the biodegradation of anthracene up to approximately 56% in 23 days. At the end of the experiment, the surface tension of culture medium decreased comparing it to the blank, indicating generation of surfactant compounds.

  19. Structural optimization with approximate sensitivities

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

    1994-01-01

    Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

  20. Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

    NASA Technical Reports Server (NTRS)

    Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

    2004-01-01

    Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

  1. Supervised learning from human performance at the computationally hard problem of optimal traffic signal control on a network of junctions

    PubMed Central

    Box, Simon

    2014-01-01

    Optimal switching of traffic lights on a network of junctions is a computationally intractable problem. In this research, road traffic networks containing signallized junctions are simulated. A computer game interface is used to enable a human ‘player’ to control the traffic light settings on the junctions within the simulation. A supervised learning approach, based on simple neural network classifiers can be used to capture human player's strategies in the game and thus develop a human-trained machine control (HuTMaC) system that approaches human levels of performance. Experiments conducted within the simulation compare the performance of HuTMaC to two well-established traffic-responsive control systems that are widely deployed in the developed world and also to a temporal difference learning-based control method. In all experiments, HuTMaC outperforms the other control methods in terms of average delay and variance over delay. The conclusion is that these results add weight to the suggestion that HuTMaC may be a viable alternative, or supplemental method, to approximate optimization for some practical engineering control problems where the optimal strategy is computationally intractable. PMID:26064570

  2. Supervised learning from human performance at the computationally hard problem of optimal traffic signal control on a network of junctions.

    PubMed

    Box, Simon

    2014-12-01

    Optimal switching of traffic lights on a network of junctions is a computationally intractable problem. In this research, road traffic networks containing signallized junctions are simulated. A computer game interface is used to enable a human 'player' to control the traffic light settings on the junctions within the simulation. A supervised learning approach, based on simple neural network classifiers can be used to capture human player's strategies in the game and thus develop a human-trained machine control (HuTMaC) system that approaches human levels of performance. Experiments conducted within the simulation compare the performance of HuTMaC to two well-established traffic-responsive control systems that are widely deployed in the developed world and also to a temporal difference learning-based control method. In all experiments, HuTMaC outperforms the other control methods in terms of average delay and variance over delay. The conclusion is that these results add weight to the suggestion that HuTMaC may be a viable alternative, or supplemental method, to approximate optimization for some practical engineering control problems where the optimal strategy is computationally intractable.

  3. Numerical solutions of a control problem governed by functional differential equations

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Thrift, P. R.; Burns, J. A.; Cliff, E. M.

    1978-01-01

    A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.

  4. Investigations of quantum heuristics for optimization

    NASA Astrophysics Data System (ADS)

    Rieffel, Eleanor; Hadfield, Stuart; Jiang, Zhang; Mandra, Salvatore; Venturelli, Davide; Wang, Zhihui

    We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

  5. Kernel-based least squares policy iteration for reinforcement learning.

    PubMed

    Xu, Xin; Hu, Dewen; Lu, Xicheng

    2007-07-01

    In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.

  6. Optimal feedback strategies for pursuit-evasion and interception in a plane

    NASA Technical Reports Server (NTRS)

    Rajan, N.; Ardema, M. D.

    1983-01-01

    Variable-speed pursuit-evasion and interception for two aircraft moving in a horizontal plane are analyzed in terms of a coordinate frame fixed in the plane at termination. Each participant's optimal motion can be represented by extremal trajectory maps. These maps are used to discuss sub-optimal approximations that are independent of the other participant. A method of constructing sections of the barrier, dispersal, and control-level surfaces and thus determining feedback strategies is described. Some examples are shown for pursuit-evasion and the minimum-time interception of a straight-flying target.

  7. Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows

    NASA Technical Reports Server (NTRS)

    Taylor, Arthur C., III; Hou, Gene W.; Korivi, Vamshi M.

    1991-01-01

    A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.

  8. Multi-AUV autonomous task planning based on the scroll time domain quantum bee colony optimization algorithm in uncertain environment

    PubMed Central

    Zhang, Rubo; Yang, Yu

    2017-01-01

    Research on distributed task planning model for multi-autonomous underwater vehicle (MAUV). A scroll time domain quantum artificial bee colony (STDQABC) optimization algorithm is proposed to solve the multi-AUV optimal task planning scheme. In the uncertain marine environment, the rolling time domain control technique is used to realize a numerical optimization in a narrowed time range. Rolling time domain control is one of the better task planning techniques, which can greatly reduce the computational workload and realize the tradeoff between AUV dynamics, environment and cost. Finally, a simulation experiment was performed to evaluate the distributed task planning performance of the scroll time domain quantum bee colony optimization algorithm. The simulation results demonstrate that the STDQABC algorithm converges faster than the QABC and ABC algorithms in terms of both iterations and running time. The STDQABC algorithm can effectively improve MAUV distributed tasking planning performance, complete the task goal and get the approximate optimal solution. PMID:29186166

  9. Multi-AUV autonomous task planning based on the scroll time domain quantum bee colony optimization algorithm in uncertain environment.

    PubMed

    Li, Jianjun; Zhang, Rubo; Yang, Yu

    2017-01-01

    Research on distributed task planning model for multi-autonomous underwater vehicle (MAUV). A scroll time domain quantum artificial bee colony (STDQABC) optimization algorithm is proposed to solve the multi-AUV optimal task planning scheme. In the uncertain marine environment, the rolling time domain control technique is used to realize a numerical optimization in a narrowed time range. Rolling time domain control is one of the better task planning techniques, which can greatly reduce the computational workload and realize the tradeoff between AUV dynamics, environment and cost. Finally, a simulation experiment was performed to evaluate the distributed task planning performance of the scroll time domain quantum bee colony optimization algorithm. The simulation results demonstrate that the STDQABC algorithm converges faster than the QABC and ABC algorithms in terms of both iterations and running time. The STDQABC algorithm can effectively improve MAUV distributed tasking planning performance, complete the task goal and get the approximate optimal solution.

  10. Suboptimal LQR-based spacecraft full motion control: Theory and experimentation

    NASA Astrophysics Data System (ADS)

    Guarnaccia, Leone; Bevilacqua, Riccardo; Pastorelli, Stefano P.

    2016-05-01

    This work introduces a real time suboptimal control algorithm for six-degree-of-freedom spacecraft maneuvering based on a State-Dependent-Algebraic-Riccati-Equation (SDARE) approach and real-time linearization of the equations of motion. The control strategy is sub-optimal since the gains of the linear quadratic regulator (LQR) are re-computed at each sample time. The cost function of the proposed controller has been compared with the one obtained via a general purpose optimal control software, showing, on average, an increase in control effort of approximately 15%, compensated by real-time implementability. Lastly, the paper presents experimental tests on a hardware-in-the-loop six-degree-of-freedom spacecraft simulator, designed for testing new guidance, navigation, and control algorithms for nano-satellites in a one-g laboratory environment. The tests show the real-time feasibility of the proposed approach.

  11. Optimization of cooling strategy and seeding by FBRM analysis of batch crystallization

    NASA Astrophysics Data System (ADS)

    Zhang, Dejiang; Liu, Lande; Xu, Shijie; Du, Shichao; Dong, Weibing; Gong, Junbo

    2018-03-01

    A method is presented for optimizing the cooling strategy and seed loading simultaneously. Focused beam reflectance measurement (FBRM) was used to determine the approximating optimal cooling profile. Using these results in conjunction with constant growth rate assumption, modified Mullin-Nyvlt trajectory could be calculated. This trajectory could suppress secondary nucleation and has the potential to control product's polymorph distribution. Comparing with linear and two step cooling, modified Mullin-Nyvlt trajectory have a larger size distribution and a better morphology. Based on the calculating results, the optimized seed loading policy was also developed. This policy could be useful for guiding the batch crystallization process.

  12. Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

    NASA Astrophysics Data System (ADS)

    Muldoon, F. H.

    2018-04-01

    Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

  13. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

    PubMed

    Wei, Qinglai; Liu, Derong; Lin, Hanquan

    2016-03-01

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  14. Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

    PubMed

    Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali

    2017-09-01

    In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

  15. A reliable algorithm for optimal control synthesis

    NASA Technical Reports Server (NTRS)

    Vansteenwyk, Brett; Ly, Uy-Loi

    1992-01-01

    In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

  16. The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

    NASA Technical Reports Server (NTRS)

    Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

    2017-01-01

    Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

  17. Safe landing area determination for a Moon lander by reachability analysis

    NASA Astrophysics Data System (ADS)

    Arslantaş, Yunus Emre; Oehlschlägel, Thimo; Sagliano, Marco

    2016-11-01

    In the last decades developments in space technology paved the way to more challenging missions like asteroid mining, space tourism and human expansion into the Solar System. These missions result in difficult tasks such as guidance schemes for re-entry, landing on celestial bodies and implementation of large angle maneuvers for spacecraft. There is a need for a safety system to increase the robustness and success of these missions. Reachability analysis meets this requirement by obtaining the set of all achievable states for a dynamical system starting from an initial condition with given admissible control inputs of the system. This paper proposes an algorithm for the approximation of nonconvex reachable sets (RS) by using optimal control. Therefore subset of the state space is discretized by equidistant points and for each grid point a distance function is defined. This distance function acts as an objective function for a related optimal control problem (OCP). Each infinite dimensional OCP is transcribed into a finite dimensional Nonlinear Programming Problem (NLP) by using Pseudospectral Methods (PSM). Finally, the NLPs are solved using available tools resulting in approximated reachable sets with information about the states of the dynamical system at these grid points. The algorithm is applied on a generic Moon landing mission. The proposed method computes approximated reachable sets and the attainable safe landing region with information about propellant consumption and time.

  18. Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

    NASA Astrophysics Data System (ADS)

    Zabolotnov, Yu. M.; Lobanov, A. A.

    2017-05-01

    A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

  19. Configuring Airspace Sectors with Approximate Dynamic Programming

    NASA Technical Reports Server (NTRS)

    Bloem, Michael; Gupta, Pramod

    2010-01-01

    In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

  20. Distributed Optimal Consensus Control for Multiagent Systems With Input Delay.

    PubMed

    Zhang, Huaipin; Yue, Dong; Zhao, Wei; Hu, Songlin; Dou, Chunxia; Huaipin Zhang; Dong Yue; Wei Zhao; Songlin Hu; Chunxia Dou; Hu, Songlin; Zhang, Huaipin; Dou, Chunxia; Yue, Dong; Zhao, Wei

    2018-06-01

    This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

  1. Near Optimal Event-Triggered Control of Nonlinear Discrete-Time Systems Using Neurodynamic Programming.

    PubMed

    Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

    2016-09-01

    This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.

  2. Monotonicity of fitness landscapes and mutation rate control.

    PubMed

    Belavkin, Roman V; Channon, Alastair; Aston, Elizabeth; Aston, John; Krašovec, Rok; Knight, Christopher G

    2016-12-01

    A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.

  3. Theory and computation of optimal low- and medium-thrust transfers

    NASA Technical Reports Server (NTRS)

    Chuang, C.-H.

    1994-01-01

    This report describes the current state of development of methods for calculating optimal orbital transfers with large numbers of burns. Reported on first is the homotopy-motivated and so-called direction correction method. So far this method has been partially tested with one solver; the final step has yet to be implemented. Second is the patched transfer method. This method is rooted in some simplifying approximations made on the original optimal control problem. The transfer is broken up into single-burn segments, each single-burn solved as a predictor step and the whole problem then solved with a corrector step.

  4. Algorithm for fuel conservative horizontal capture trajectories

    NASA Technical Reports Server (NTRS)

    Neuman, F.; Erzberger, H.

    1981-01-01

    A real time algorithm for computing constant altitude fuel-conservative approach trajectories for aircraft is described. The characteristics of the trajectory computed were chosen to approximate the extremal trajectories obtained from the optimal control solution to the problem and showed a fuel difference of only 0.5 to 2 percent for the real time algorithm in favor of the extremals. The trajectories may start at any initial position, heading, and speed and end at any other final position, heading, and speed. They consist of straight lines and a series of circular arcs of varying radius to approximate constant bank-angle decelerating turns. Throttle control is maximum thrust, nominal thrust, or zero thrust. Bank-angle control is either zero or aproximately 30 deg.

  5. Variational Trajectory Optimization Tool Set: Technical description and user's manual

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Queen, Eric M.; Cavanaugh, Michael D.; Wetzel, Todd A.; Moerder, Daniel D.

    1993-01-01

    The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

  6. Fully probabilistic control design in an adaptive critic framework.

    PubMed

    Herzallah, Randa; Kárný, Miroslav

    2011-12-01

    Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem; in particular, very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic control algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this paper. Copyright © 2011 Elsevier Ltd. All rights reserved.

  7. Peak-Seeking Control For Reduced Fuel Consumption: Flight-Test Results For The Full-Scale Advanced Systems Testbed FA-18 Airplane

    NASA Technical Reports Server (NTRS)

    Brown, Nelson

    2013-01-01

    A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. This presentation also focuses on the design of the flight experiment and the practical challenges of conducting the experiment.

  8. Development of an adaptive hp-version finite element method for computational optimal control

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Warner, Michael S.

    1994-01-01

    In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

  9. Method for depleting BWRs using optimal control rod patterns

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Taner, M.S.; Levine, S.H.; Hsiao, M.Y.

    1991-01-01

    Control rod (CR) programming is an essential core management activity for boiling water reactors (BWRs). After establishing a core reload design for a BWR, CR programming is performed to develop a sequence of exposure-dependent CR patterns that assure the safe and effective depletion of the core through a reactor cycle. A time-variant target power distribution approach has been assumed in this study. The authors have developed OCTOPUS to implement a new two-step method for designing semioptimal CR programs for BWRs. The optimization procedure of OCTOPUS is based on the method of approximation programming and uses the SIMULATE-E code for nucleonicsmore » calculations.« less

  10. SaaS enabled admission control for MCMC simulation in cloud computing infrastructures

    NASA Astrophysics Data System (ADS)

    Vázquez-Poletti, J. L.; Moreno-Vozmediano, R.; Han, R.; Wang, W.; Llorente, I. M.

    2017-02-01

    Markov Chain Monte Carlo (MCMC) methods are widely used in the field of simulation and modelling of materials, producing applications that require a great amount of computational resources. Cloud computing represents a seamless source for these resources in the form of HPC. However, resource over-consumption can be an important drawback, specially if the cloud provision process is not appropriately optimized. In the present contribution we propose a two-level solution that, on one hand, takes advantage of approximate computing for reducing the resource demand and on the other, uses admission control policies for guaranteeing an optimal provision to running applications.

  11. Ab initio design of laser pulses to control molecular motion

    NASA Astrophysics Data System (ADS)

    Balint-Kurti, Gabriel; Ren, Qinghua; Manby, Frederick; Artamonov, Maxim; Ho, Tak-San; Rabitz, Herschel; Zou, Shiyang; Singh, Harjinder

    2007-03-01

    Our recent attempts to design laser pulses entirely theoretically, in a quantitative and accurate manner, so as to fully understand the underlying mechanisms active in the control process will be outlined. We have developed a new Born-Oppenheimer like separation called the electric-nuclear Born-Oppenheimer (ENBO) approximation. In this approximation variations of both the nuclear geometry and of the external electric field are assumed to be slow compared with the speed at which the electronic degrees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei, but also on the electric field strength and on the orientation of the molecule with respect to the electric field. The range of validity of the ENBO approximation is discussed. Optimal control theory is used along with the ENBO approximation to design laser pulses for exciting vibrational and rotational motion in H2 and CO molecules. Progress on other applications, including controlling photodissociation processes, isotope separation, stabilization of molecular Bose-Einstein condensates as well as applications to biological molecules also be presented. *Support acknowledged from EPSRC.

  12. PSO-based PID Speed Control of Traveling Wave Ultrasonic Motor under Temperature Disturbance

    NASA Astrophysics Data System (ADS)

    Arifin Mat Piah, Kamal; Yusoff, Wan Azhar Wan; Azmi, Nur Iffah Mohamed; Romlay, Fadhlur Rahman Mohd

    2018-03-01

    Traveling wave ultrasonic motors (TWUSMs) have a time varying dynamics characteristics. Temperature rise in TWUSMs remains a problem particularly in sustaining optimum speed performance. In this study, a PID controller is used to control the speed of TWUSM under temperature disturbance. Prior to developing the controller, a linear approximation model which relates the speed to the temperature is developed based on the experimental data. Two tuning methods are used to determine PID parameters: conventional Ziegler-Nichols(ZN) and particle swarm optimization (PSO). The comparison of speed control performance between PSO-PID and ZN-PID is presented. Modelling, simulation and experimental work is carried out utilizing Fukoku-Shinsei USR60 as the chosen TWUSM. The results of the analyses and experimental work reveal that PID tuning using PSO-based optimization has the advantage over the conventional Ziegler-Nichols method.

  13. Solution to automatic generation control problem using firefly algorithm optimized I(λ)D(µ) controller.

    PubMed

    Debbarma, Sanjoy; Saikia, Lalit Chandra; Sinha, Nidul

    2014-03-01

    Present work focused on automatic generation control (AGC) of a three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRC). A fractional order (FO) controller named as I(λ)D(µ) controller based on crone approximation is proposed for the first time as an appropriate technique to solve the multi-area AGC problem in power systems. A recently developed metaheuristic algorithm known as firefly algorithm (FA) is used for the simultaneous optimization of the gains and other parameters such as order of integrator (λ) and differentiator (μ) of I(λ)D(µ) controller and governor speed regulation parameters (R). The dynamic responses corresponding to optimized I(λ)D(µ) controller gains, λ, μ, and R are compared with that of classical integer order (IO) controllers such as I, PI and PID controllers. Simulation results show that the proposed I(λ)D(µ) controller provides more improved dynamic responses and outperforms the IO based classical controllers. Further, sensitivity analysis confirms the robustness of the so optimized I(λ)D(µ) controller to wide changes in system loading conditions and size and position of SLP. Proposed controller is also found to have performed well as compared to IO based controllers when SLP takes place simultaneously in any two areas or all the areas. Robustness of the proposed I(λ)D(µ) controller is also tested against system parameter variations. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Heuristic and optimal policy computations in the human brain during sequential decision-making.

    PubMed

    Korn, Christoph W; Bach, Dominik R

    2018-01-23

    Optimal decisions across extended time horizons require value calculations over multiple probabilistic future states. Humans may circumvent such complex computations by resorting to easy-to-compute heuristics that approximate optimal solutions. To probe the potential interplay between heuristic and optimal computations, we develop a novel sequential decision-making task, framed as virtual foraging in which participants have to avoid virtual starvation. Rewards depend only on final outcomes over five-trial blocks, necessitating planning over five sequential decisions and probabilistic outcomes. Here, we report model comparisons demonstrating that participants primarily rely on the best available heuristic but also use the normatively optimal policy. FMRI signals in medial prefrontal cortex (MPFC) relate to heuristic and optimal policies and associated choice uncertainties. Crucially, reaction times and dorsal MPFC activity scale with discrepancies between heuristic and optimal policies. Thus, sequential decision-making in humans may emerge from integration between heuristic and optimal policies, implemented by controllers in MPFC.

  15. Approximate solution of space and time fractional higher order phase field equation

    NASA Astrophysics Data System (ADS)

    Shamseldeen, S.

    2018-03-01

    This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

  16. Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

    DTIC Science & Technology

    2010-01-01

    1996; Elgart and Kamenev, 2004). Instead, in this article, we will employ an eikonal approximation to recast the problem in terms of an effective...a control strategy on the extinction rate can be determined by its effect on the optimal path (Dykman et al., 2008). Through the use of the eikonal ...the solution of Eqs. (6a)–(6b) in the eikonal form (Elgart and Kamenev, 2004; Doering et al., 2005; Kubo et al., 1973; Wentzell, 1976; Gang, 1987

  17. Nonlinear identification using a B-spline neural network and chaotic immune approaches

    NASA Astrophysics Data System (ADS)

    dos Santos Coelho, Leandro; Pessôa, Marcelo Wicthoff

    2009-11-01

    One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to "learn" the process model from input-output data or "learn" fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method - the opt-aiNet - combined with sequences generate by Hénon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.

  18. The effect of Fisher information matrix approximation methods in population optimal design calculations.

    PubMed

    Strömberg, Eric A; Nyberg, Joakim; Hooker, Andrew C

    2016-12-01

    With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

  19. Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-Test Results

    NASA Technical Reports Server (NTRS)

    Brown, Nelson Andrew; Schaefer, Jacob Robert

    2013-01-01

    A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

  20. Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-test Results

    NASA Technical Reports Server (NTRS)

    Brown, Nelson Andrew; Schaefer, Jacob Robert

    2013-01-01

    A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

  1. Extracting motor synergies from random movements for low-dimensional task-space control of musculoskeletal robots.

    PubMed

    Fu, Kin Chung Denny; Dalla Libera, Fabio; Ishiguro, Hiroshi

    2015-10-08

    In the field of human motor control, the motor synergy hypothesis explains how humans simplify body control dimensionality by coordinating groups of muscles, called motor synergies, instead of controlling muscles independently. In most applications of motor synergies to low-dimensional control in robotics, motor synergies are extracted from given optimal control signals. In this paper, we address the problems of how to extract motor synergies without optimal data given, and how to apply motor synergies to achieve low-dimensional task-space tracking control of a human-like robotic arm actuated by redundant muscles, without prior knowledge of the robot. We propose to extract motor synergies from a subset of randomly generated reaching-like movement data. The essence is to first approximate the corresponding optimal control signals, using estimations of the robot's forward dynamics, and to extract the motor synergies subsequently. In order to avoid modeling difficulties, a learning-based control approach is adopted such that control is accomplished via estimations of the robot's inverse dynamics. We present a kernel-based regression formulation to estimate the forward and the inverse dynamics, and a sliding controller in order to cope with estimation error. Numerical evaluations show that the proposed method enables extraction of motor synergies for low-dimensional task-space control.

  2. Optimal initiation of electronic excited state mediated intramolecular H-transfer in malonaldehyde by UV-laser pulses

    NASA Astrophysics Data System (ADS)

    Nandipati, K. R.; Singh, H.; Nagaprasad Reddy, S.; Kumar, K. A.; Mahapatra, S.

    2014-12-01

    Optimally controlled initiation of intramolecular H-transfer in malonaldehyde is accomplished by designing a sequence of ultrashort (~80 fs) down-chirped pump-dump ultra violet (UV)-laser pulses through an optically bright electronic excited [ S 2 ( π π ∗)] state as a mediator. The sequence of such laser pulses is theoretically synthesized within the framework of optimal control theory (OCT) and employing the well-known pump-dump scheme of Tannor and Rice [D.J. Tannor, S.A. Rice, J. Chem. Phys. 83, 5013 (1985)]. In the OCT, the control task is framed as the maximization of cost functional defined in terms of an objective function along with the constraints on the field intensity and system dynamics. The latter is monitored by solving the time-dependent Schrödinger equation. The initial guess, laser driven dynamics and the optimized pulse structure (i.e., the spectral content and temporal profile) followed by associated mechanism involved in fulfilling the control task are examined in detail and discussed. A comparative account of the dynamical outcomes within the Condon approximation for the transition dipole moment versus its more realistic value calculated ab initio is also presented.

  3. A roadmap for optimal control: the right way to commute.

    PubMed

    Ross, I Michael

    2005-12-01

    Optimal control theory is the foundation for many problems in astrodynamics. Typical examples are trajectory design and optimization, relative motion control of distributed space systems and attitude steering. Many such problems in astrodynamics are solved by an alternative route of mathematical analysis and deep physical insight, in part because of the perception that an optimal control framework generates hard problems. Although this is indeed true of the Bellman and Pontryagin frameworks, the covector mapping principle provides a neoclassical approach that renders hard problems easy. That is, although the origins of this philosophy can be traced back to Bernoulli and Euler, it is essentially modern as a result of the strong linkage between approximation theory, set-valued analysis and computing technology. Motivated by the broad success of this approach, mission planners are now conceiving and demanding higher performance from space systems. This has resulted in new set of theoretical and computational problems. Recently, under the leadership of NASA-GRC, several workshops were held to address some of these problems. This paper outlines the theoretical issues stemming from practical problems in astrodynamics. Emphasis is placed on how it pertains to advanced mission design problems.

  4. An application of forward-backward difference approximation method on the optimal control problem in the transmission of tuberculosis model

    NASA Astrophysics Data System (ADS)

    Rahmah, Z.; Subartini, B.; Djauhari, E.; Anggriani, N.; Supriatna, A. K.

    2017-03-01

    Tuberculosis (TB) is a disease that is infected by the bacteria Mycobacterium tuberculosis. The World Health Organization (WHO) recommends to implement the Baccilus Calmete Guerin (BCG) vaccine in toddler aged two to three months to be protected from the infection. This research explores the numerical simulation of forward-backward difference approximation method on the model of TB transmission considering this vaccination program. The model considers five compartments of sub-populations, i.e. susceptible, vaccinated, exposed, infected, and recovered human sub-populations. We consider here the vaccination as a control variable. The results of the simulation showed that vaccination can indeed reduce the number of infected human population.

  5. Optimization of a pH-shift control strategy for producing monoclonal antibodies in Chinese hamster ovary cell cultures using a pH-dependent dynamic model.

    PubMed

    Hogiri, Tomoharu; Tamashima, Hiroshi; Nishizawa, Akitoshi; Okamoto, Masahiro

    2018-02-01

    To optimize monoclonal antibody (mAb) production in Chinese hamster ovary cell cultures, culture pH should be temporally controlled with high resolution. In this study, we propose a new pH-dependent dynamic model represented by simultaneous differential equations including a minimum of six system component, depending on pH value. All kinetic parameters in the dynamic model were estimated using an evolutionary numerical optimization (real-coded genetic algorithm) method based on experimental time-course data obtained at different pH values ranging from 6.6 to 7.2. We determined an optimal pH-shift schedule theoretically. We validated this optimal pH-shift schedule experimentally and mAb production increased by approximately 40% with this schedule. Throughout this study, it was suggested that the culture pH-shift optimization strategy using a pH-dependent dynamic model is suitable to optimize any pH-shift schedule for CHO cell lines used in mAb production projects. Copyright © 2017 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

  6. Reliability-based design optimization using a generalized subset simulation method and posterior approximation

    NASA Astrophysics Data System (ADS)

    Ma, Yuan-Zhuo; Li, Hong-Shuang; Yao, Wei-Xing

    2018-05-01

    The evaluation of the probabilistic constraints in reliability-based design optimization (RBDO) problems has always been significant and challenging work, which strongly affects the performance of RBDO methods. This article deals with RBDO problems using a recently developed generalized subset simulation (GSS) method and a posterior approximation approach. The posterior approximation approach is used to transform all the probabilistic constraints into ordinary constraints as in deterministic optimization. The assessment of multiple failure probabilities required by the posterior approximation approach is achieved by GSS in a single run at all supporting points, which are selected by a proper experimental design scheme combining Sobol' sequences and Bucher's design. Sequentially, the transformed deterministic design optimization problem can be solved by optimization algorithms, for example, the sequential quadratic programming method. Three optimization problems are used to demonstrate the efficiency and accuracy of the proposed method.

  7. Neural-network-based navigation and control of unmanned aerial vehicles for detecting unintended emissions

    NASA Astrophysics Data System (ADS)

    Zargarzadeh, H.; Nodland, David; Thotla, V.; Jagannathan, S.; Agarwal, S.

    2012-06-01

    Unmanned Aerial Vehicles (UAVs) are versatile aircraft with many applications, including the potential for use to detect unintended electromagnetic emissions from electronic devices. A particular area of recent interest has been helicopter unmanned aerial vehicles. Because of the nature of these helicopters' dynamics, high-performance controller design for them presents a challenge. This paper introduces an optimal controller design via output feedback control for trajectory tracking of a helicopter UAV using a neural network (NN). The output-feedback control system utilizes the backstepping methodology, employing kinematic, virtual, and dynamic controllers and an observer. Optimal tracking is accomplished with a single NN utilized for cost function approximation. The controller positions the helicopter, which is equipped with an antenna, such that the antenna can detect unintended emissions. The overall closed-loop system stability with the proposed controller is demonstrated by using Lyapunov analysis. Finally, results are provided to demonstrate the effectiveness of the proposed control design for positioning the helicopter for unintended emissions detection.

  8. Flutter suppression control law synthesis for the Active Flexible Wing model

    NASA Technical Reports Server (NTRS)

    Mukhopadhyay, Vivek; Perry, Boyd, III; Noll, Thomas E.

    1989-01-01

    The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.

  9. Stochastic approximation methods-Powerful tools for simulation and optimization: A survey of some recent work on multi-agent systems and cyber-physical systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yin, George; Wang, Le Yi; Zhang, Hongwei

    2014-12-10

    Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomlymore » switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.« less

  10. Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

    NASA Technical Reports Server (NTRS)

    Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

    1998-01-01

    Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

  11. Event-Triggered Adaptive Dynamic Programming for Continuous-Time Systems With Control Constraints.

    PubMed

    Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

    2016-08-31

    In this paper, an event-triggered near optimal control structure is developed for nonlinear continuous-time systems with control constraints. Due to the saturating actuators, a nonquadratic cost function is introduced and the Hamilton-Jacobi-Bellman (HJB) equation for constrained nonlinear continuous-time systems is formulated. In order to solve the HJB equation, an actor-critic framework is presented. The critic network is used to approximate the cost function and the action network is used to estimate the optimal control law. In addition, in the proposed method, the control signal is transmitted in an aperiodic manner to reduce the computational and the transmission cost. Both the networks are only updated at the trigger instants decided by the event-triggered condition. Detailed Lyapunov analysis is provided to guarantee that the closed-loop event-triggered system is ultimately bounded. Three case studies are used to demonstrate the effectiveness of the proposed method.

  12. Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Killingsworth, W. R., Jr.

    1972-01-01

    The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

  13. A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Grunberg, D. B.

    1986-01-01

    A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

  14. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

    1989-01-01

    A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

  15. Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

    NASA Technical Reports Server (NTRS)

    Calise, A. J.; Corban, J. E.

    1990-01-01

    The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

  16. Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

    NASA Technical Reports Server (NTRS)

    Fadel, G. M.

    1991-01-01

    The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

  17. Rational positive real approximations for LQG optimal compensators arising in active stabilization of flexible structures

    NASA Technical Reports Server (NTRS)

    Desantis, A.

    1994-01-01

    In this paper the approximation problem for a class of optimal compensators for flexible structures is considered. The particular case of a simply supported truss with an offset antenna is dealt with. The nonrational positive real optimal compensator transfer function is determined, and it is proposed that an approximation scheme based on a continued fraction expansion method be used. Comparison with the more popular modal expansion technique is performed in terms of stability margin and parameters sensitivity of the relative approximated closed loop transfer functions.

  18. Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

    NASA Technical Reports Server (NTRS)

    Tiffany, Sherwood H.; Adams, William M., Jr.

    1988-01-01

    The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

  19. Optimal Budget Allocation for Sample Average Approximation

    DTIC Science & Technology

    2011-06-01

    an optimization algorithm applied to the sample average problem. We examine the convergence rate of the estimator as the computing budget tends to...regime for the optimization algorithm . 1 Introduction Sample average approximation (SAA) is a frequently used approach to solving stochastic programs...appealing due to its simplicity and the fact that a large number of standard optimization algorithms are often available to optimize the resulting sample

  20. Effective algorithm for solving complex problems of production control and of material flows control of industrial enterprise

    NASA Astrophysics Data System (ADS)

    Mezentsev, Yu A.; Baranova, N. V.

    2018-05-01

    A universal economical and mathematical model designed for determination of optimal strategies for managing subsystems (components of subsystems) of production and logistics of enterprises is considered. Declared universality allows taking into account on the system level both production components, including limitations on the ways of converting raw materials and components into sold goods, as well as resource and logical restrictions on input and output material flows. The presented model and generated control problems are developed within the framework of the unified approach that allows one to implement logical conditions of any complexity and to define corresponding formal optimization tasks. Conceptual meaning of used criteria and limitations are explained. The belonging of the generated tasks of the mixed programming with the class of NP is shown. An approximate polynomial algorithm for solving the posed optimization tasks for mixed programming of real dimension with high computational complexity is proposed. Results of testing the algorithm on the tasks in a wide range of dimensions are presented.

  1. Microgrid energy dispatching for industrial zones with renewable generations and electric vehicles via stochastic optimization and learning

    NASA Astrophysics Data System (ADS)

    Zhang, Kai; Li, Jingzhi; He, Zhubin; Yan, Wanfeng

    2018-07-01

    In this paper, a stochastic optimization framework is proposed to address the microgrid energy dispatching problem with random renewable generation and vehicle activity pattern, which is closer to the practical applications. The patterns of energy generation, consumption and storage availability are all random and unknown at the beginning, and the microgrid controller design (MCD) is formulated as a Markov decision process (MDP). Hence, an online learning-based control algorithm is proposed for the microgrid, which could adapt the control policy with increasing knowledge of the system dynamics and converges to the optimal algorithm. We adopt the linear approximation idea to decompose the original value functions as the summation of each per-battery value function. As a consequence, the computational complexity is significantly reduced from exponential growth to linear growth with respect to the size of battery states. Monte Carlo simulation of different scenarios demonstrates the effectiveness and efficiency of our algorithm.

  2. Approximate Optimal Control as a Model for Motor Learning

    ERIC Educational Resources Information Center

    Berthier, Neil E.; Rosenstein, Michael T.; Barto, Andrew G.

    2005-01-01

    Current models of psychological development rely heavily on connectionist models that use supervised learning. These models adapt network weights when the network output does not match the target outputs computed by some agent. The authors present a model of motor learning in which the child uses exploration to discover appropriate ways of…

  3. Using Approximations to Accelerate Engineering Design Optimization

    NASA Technical Reports Server (NTRS)

    Torczon, Virginia; Trosset, Michael W.

    1998-01-01

    Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

  4. Quantum approximate optimization algorithm for MaxCut: A fermionic view

    NASA Astrophysics Data System (ADS)

    Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

    2018-02-01

    Farhi et al. recently proposed a class of quantum algorithms, the quantum approximate optimization algorithm (QAOA), for approximately solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028; arXiv:1412.6062; arXiv:1602.07674). A level-p QAOA circuit consists of p steps; in each step a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2 p times for which these two Hamiltonians are applied are the parameters of the algorithm, which are to be optimized classically for the best performance. As p increases, parameter optimization becomes inefficient due to the curse of dimensionality. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here we analytically and numerically study parameter setting for the QAOA applied to MaxCut. For the level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MaxCut, the "ring of disagrees," or the one-dimensional antiferromagnetic ring, we provide an analysis for an arbitrarily high level. Using a fermionic representation, the evolution of the system under the QAOA translates into quantum control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of the QAOA for any p . It also greatly simplifies the numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional submanifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

  5. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

    NASA Astrophysics Data System (ADS)

    Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.

    2018-01-01

    We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  6. On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

  7. Minimum-fuel turning climbout and descent guidance of transport jets

    NASA Technical Reports Server (NTRS)

    Neuman, F.; Kreindler, E.

    1983-01-01

    The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft.

  8. Feedback laws for fuel minimization for transport aircraft

    NASA Technical Reports Server (NTRS)

    Price, D. B.; Gracey, C.

    1984-01-01

    The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

  9. A rotor optimization using regression analysis

    NASA Technical Reports Server (NTRS)

    Giansante, N.

    1984-01-01

    The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

  10. Generation of optimal artificial neural networks using a pattern search algorithm: application to approximation of chemical systems.

    PubMed

    Ihme, Matthias; Marsden, Alison L; Pitsch, Heinz

    2008-02-01

    A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization. When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function, and the connectivity among neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrates equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully connected feedforward network having four nonlinear hidden layers and 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 x 500 grid point discretization of the parameter space.

  11. Time Varying Compensator Design for Reconfigurable Structures Using Non-Collocated Feedback

    NASA Technical Reports Server (NTRS)

    Scott, Michael A.

    1996-01-01

    Analysis and synthesis tools are developed to improved the dynamic performance of reconfigurable nonminimum phase, nonstrictly positive real-time variant systems. A novel Spline Varying Optimal (SVO) controller is developed for the kinematic nonlinear system. There are several advantages to using the SVO controller, in which the spline function approximates the system model, observer, and controller gain. They are: The spline function approximation is simply connected, thus the SVO controller is more continuous than traditional gain scheduled controllers when implemented on a time varying plant; ft is easier for real-time implementations in storage and computational effort; where system identification is required, the spline function requires fewer experiments, namely four experiments; and initial startup estimator transients are eliminated. The SVO compensator was evaluated on a high fidelity simulation of the Shuttle Remote Manipulator System. The SVO controller demonstrated significant improvement over the present arm performance: (1) Damping level was improved by a factor of 3; and (2) Peak joint torque was reduced by a factor of 2 following Shuttle thruster firings.

  12. Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR.

    PubMed

    Skinner, Thomas E; Reiss, Timo O; Luy, Burkhard; Khaneja, Navin; Glaser, Steffen J

    2003-07-01

    Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.

  13. Breaking down patient and physician barriers to optimize glycemic control in type 2 diabetes.

    PubMed

    Ross, Stuart A

    2013-09-01

    Approximately half of patients with type 2 diabetes (T2D) do not achieve globally recognized blood glucose targets, despite the availability of a wide range of effective glucose-lowering therapies. Failure to maintain good glycemic control increases the risk of diabetes-related complications and long-term health care costs. Patients must be brought under glycemic control to improve treatment outcomes, but existing barriers to optimizing glycemic control must first be overcome, including patient nonadherence to treatment, the failure of physicians to intensify therapy in a timely manner, and inadequacies in the health care system itself. The reasons for such barriers include treatment side effects, complex treatment regimens, needle anxiety, poor patient education, and the absence of an adequate patient care plan; however, newer therapies and devices, combined with comprehensive care plans involving adequate patient education, can help to minimize barriers and improve treatment outcomes. Copyright © 2013 Elsevier Inc. All rights reserved.

  14. Decentralized Bayesian search using approximate dynamic programming methods.

    PubMed

    Zhao, Yijia; Patek, Stephen D; Beling, Peter A

    2008-08-01

    We consider decentralized Bayesian search problems that involve a team of multiple autonomous agents searching for targets on a network of search points operating under the following constraints: 1) interagent communication is limited; 2) the agents do not have the opportunity to agree in advance on how to resolve equivalent but incompatible strategies; and 3) each agent lacks the ability to control or predict with certainty the actions of the other agents. We formulate the multiagent search-path-planning problem as a decentralized optimal control problem and introduce approximate dynamic heuristics that can be implemented in a decentralized fashion. After establishing some analytical properties of the heuristics, we present computational results for a search problem involving two agents on a 5 x 5 grid.

  15. Robust Optimization Design for Turbine Blade-Tip Radial Running Clearance using Hierarchically Response Surface Method

    NASA Astrophysics Data System (ADS)

    Zhiying, Chen; Ping, Zhou

    2017-11-01

    Considering the robust optimization computational precision and efficiency for complex mechanical assembly relationship like turbine blade-tip radial running clearance, a hierarchically response surface robust optimization algorithm is proposed. The distribute collaborative response surface method is used to generate assembly system level approximation model of overall parameters and blade-tip clearance, and then a set samples of design parameters and objective response mean and/or standard deviation is generated by using system approximation model and design of experiment method. Finally, a new response surface approximation model is constructed by using those samples, and this approximation model is used for robust optimization process. The analyses results demonstrate the proposed method can dramatic reduce the computational cost and ensure the computational precision. The presented research offers an effective way for the robust optimization design of turbine blade-tip radial running clearance.

  16. A Rigorous Framework for Optimization of Expensive Functions by Surrogates

    NASA Technical Reports Server (NTRS)

    Booker, Andrew J.; Dennis, J. E., Jr.; Frank, Paul D.; Serafini, David B.; Torczon, Virginia; Trosset, Michael W.

    1998-01-01

    The goal of the research reported here is to develop rigorous optimization algorithms to apply to some engineering design problems for which design application of traditional optimization approaches is not practical. This paper presents and analyzes a framework for generating a sequence of approximations to the objective function and managing the use of these approximations as surrogates for optimization. The result is to obtain convergence to a minimizer of an expensive objective function subject to simple constraints. The approach is widely applicable because it does not require, or even explicitly approximate, derivatives of the objective. Numerical results are presented for a 31-variable helicopter rotor blade design example and for a standard optimization test example.

  17. Optimal guidance law development for an advanced launch system

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Hodges, Dewey H.; Leung, Martin S.; Bless, Robert R.

    1991-01-01

    The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

  18. Parameter identification in ODE models with oscillatory dynamics: a Fourier regularization approach

    NASA Astrophysics Data System (ADS)

    Chiara D'Autilia, Maria; Sgura, Ivonne; Bozzini, Benedetto

    2017-12-01

    In this paper we consider a parameter identification problem (PIP) for data oscillating in time, that can be described in terms of the dynamics of some ordinary differential equation (ODE) model, resulting in an optimization problem constrained by the ODEs. In problems with this type of data structure, simple application of the direct method of control theory (discretize-then-optimize) yields a least-squares cost function exhibiting multiple ‘low’ minima. Since in this situation any optimization algorithm is liable to fail in the approximation of a good solution, here we propose a Fourier regularization approach that is able to identify an iso-frequency manifold {{ S}} of codimension-one in the parameter space \

  19. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1985-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  20. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  1. Minimum-Time and Vibration Avoidance Attitude Maneuver for Spacecraft with Torque and Momentum Limit Constraints in Redundant Reaction Wheel Configuration

    NASA Technical Reports Server (NTRS)

    Ha, Kong Q.; Femiano, Michael D.; Mosier, Gary E.

    2004-01-01

    In this paper, we present an optimal open-loop slew trajectory algorithm developed at GSFC for the so-called "Yardstick design" of the James Webb Space Telescope (JWST). JWST is an orbiting infrared observatory featuring a lightweight, segmented primary mirror approximately 6 meters in diameter and a sunshield approximately the size of a tennis court. This large, flexible structure will have significant number of lightly damped, dominant flexible modes. With very stringent requirements on pointing accuracy and image quality, it is important that slewing be done within the required time constraint and with minimal induced vibration in order to maximize observing efficiency. With reaction wheels as control actuators, initial wheel speeds as well as individual wheel torque and momentum limits become dominant constraints in slew performance. These constraints must be taken into account when performing slews to ensure that unexpected reaction wheel saturation does not occur, since such saturation leads to control failure in accurately tracking commanded motion and produces high frequency torque components capable of exciting structural modes. A minimum-time constraint is also included and coupled with reaction wheel limit constraints in the optimization to minimize both the effect of the control torque on the flexible body motion and the maneuver time. The optimization is on slew command parameters, such as maximum slew velocity and acceleration, for a given redundant reaction wheel configuration and is based on the dynamic interaction between the spacecraft and reaction wheel motion. Analytical development of the slew algorithm to generate desired slew position, rate, and acceleration profiles to command a feedback/feed forward control system is described. High-fidelity simulation and experimental results are presented to show that the developed slew law achieves the objectives.

  2. Numerical study on the influence of boss cap fins on efficiency of controllable-pitch propeller

    NASA Astrophysics Data System (ADS)

    Xiong, Ying; Wang, Zhanzhi; Qi, Wanjiang

    2013-03-01

    Numerical simulation is investigated to disclose how propeller boss cap fins (PBCF) operate utilizing Reynolds-averaged Navier-Stokes (RANS) method. In addition, exploration of the influencing mechanism of PBCF on the open water efficiency of one controllable-pitch propeller is analyzed through the open water characteristic curves, blade surface pressure distribution and hub streamline distribution. On this basis, the influence of parameters including airfoil profile, diameter, axial position of installation and circumferential installation angle on the open water efficiency of the controllable-pitch propeller is investigated. Numerical results show: for the controllable-pitch propeller, the thrust generated is at the optimum when the radius of boss cap fins is 1.5 times of propeller hub with an optimal installation position in the axial direction, and its optimal circumferential installation position is the midpoint of the extension line of the front and back ends of two adjacent propeller roots in the front of fin root. Under these optimal parameters, the gain of open water efficiency of the controllable-pitch propeller with different advance velocity coefficients is greater than 0.01, which accounts for approximately an increase of 1%-5% of open water efficiency.

  3. The economics of optimal urban groundwater management in southwestern USA

    NASA Astrophysics Data System (ADS)

    Hansen, Jason K.

    2012-08-01

    Groundwater serves as the primary water source for approximately 80% of public water systems in the United States, and for many more as a secondary source. Traditionally management relies on groundwater to meet rising demand by increasing supply, but climate uncertainty and population growth require more judicious management to achieve efficiency and sustainability. Over-pumping leads to groundwater overdraft and jeopardizes the ability of future users to depend on the resource. Optimal urban groundwater pumping can play a role in solving this conundrum. This paper investigates to what extent and under what circumstances controlled pumping improves social welfare. It considers management in a hydro-economic framework and finds the optimal pumping path and the optimal price path. These allow for the identification of the social benefit of controlled pumping, and the scarcity rent, which is one tool to sustainably manage groundwater resources. The model is numerically illustrated with a case study from Albuquerque, New Mexico (USA). The Albuquerque results indicate that, in the presence of strong demand growth, controlled pumping improves social welfare by 22%, extends use of the resource, and provides planners with a mechanism to advance the economic sustainability of groundwater.

  4. Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

    NASA Astrophysics Data System (ADS)

    Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Chen, Zhuo; Wang, Jin-liang

    2018-05-01

    Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R OF), flux rate (R F), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R OF, R F, and T should be controlled at approximately 156 Nm3/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

  5. A nonlinear H-infinity approach to optimal control of the depth of anaesthesia

    NASA Astrophysics Data System (ADS)

    Rigatos, Gerasimos; Rigatou, Efthymia; Zervos, Nikolaos

    2016-12-01

    Controlling the level of anaesthesia is important for improving the success rate of surgeries and for reducing the risks to which operated patients are exposed. This paper proposes a nonlinear H-infinity approach to optimal control of the level of anaesthesia. The dynamic model of the anaesthesia, which describes the concentration of the anaesthetic drug in different parts of the body, is subjected to linearization at local operating points. These are defined at each iteration of the control algorithm and consist of the present value of the system's state vector and of the last control input that was exerted on it. For this linearization Taylor series expansion is performed and the system's Jacobian matrices are computed. For the linearized model an H-infinity controller is designed. The feedback control gains are found by solving at each iteration of the control algorithm an algebraic Riccati equation. The modelling errors due to this approximate linearization are considered as disturbances which are compensated by the robustness of the control loop. The stability of the control loop is confirmed through Lyapunov analysis.

  6. Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

    NASA Astrophysics Data System (ADS)

    Sumin, M. I.

    2015-06-01

    A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

  7. Use of information entropy measures of sitting postural sway to quantify developmental delay in infants

    PubMed Central

    Deffeyes, Joan E; Harbourne, Regina T; DeJong, Stacey L; Kyvelidou, Anastasia; Stuberg, Wayne A; Stergiou, Nicholas

    2009-01-01

    Background By quantifying the information entropy of postural sway data, the complexity of the postural movement of different populations can be assessed, giving insight into pathologic motor control functioning. Methods In this study, developmental delay of motor control function in infants was assessed by analysis of sitting postural sway data acquired from force plate center of pressure measurements. Two types of entropy measures were used: symbolic entropy, including a new asymmetric symbolic entropy measure, and approximate entropy, a more widely used entropy measure. For each method of analysis, parameters were adjusted to optimize the separation of the results from the infants with delayed development from infants with typical development. Results The method that gave the widest separation between the populations was the asymmetric symbolic entropy method, which we developed by modification of the symbolic entropy algorithm. The approximate entropy algorithm also performed well, using parameters optimized for the infant sitting data. The infants with delayed development were found to have less complex patterns of postural sway in the medial-lateral direction, and were found to have different left-right symmetry in their postural sway, as compared to typically developing infants. Conclusion The results of this study indicate that optimization of the entropy algorithm for infant sitting postural sway data can greatly improve the ability to separate the infants with developmental delay from typically developing infants. PMID:19671183

  8. Optimal Keno Strategies and the Central Limit Theorem

    ERIC Educational Resources Information Center

    Johnson, Roger W.

    2006-01-01

    For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

  9. Discretized energy minimization in a wave guide with point sources

    NASA Technical Reports Server (NTRS)

    Propst, G.

    1994-01-01

    An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

  10. The linear regulator problem for parabolic systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1983-01-01

    An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

  11. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    PubMed

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  12. Nonlinear dynamic analysis and robust controller design for Francis hydraulic turbine regulating system with a straight-tube surge tank

    NASA Astrophysics Data System (ADS)

    Liang, Ji; Yuan, Xiaohui; Yuan, Yanbin; Chen, Zhihuan; Li, Yuanzheng

    2017-02-01

    The safety and stability of hydraulic turbine regulating system (HTRS) in hydropower plants become increasingly important since the rapid development and the broad application of hydro energy technology. In this paper, a novel mathematical model of Francis hydraulic turbine regulating system with a straight-tube surge tank based on a few state-space equations is introduced to study the dynamic behaviors of the HTRS system, where the existence of possible unstable oscillations of this model is studied extensively and presented in the forms of the bifurcation diagram, time waveform plot, phase trajectories, and power spectrum. To eliminate these undesirable behaviors, a specified fuzzy sliding mode controller is designed. In this hybrid controller, the sliding mode control law makes full use of the proposed model to guarantee the robust control in the presence of system uncertainties, while the fuzzy system is applied to approximate the proper gains of the switching control in sliding mode technique to reduce the chattering effect, and particle swarm optimization is developed to search the optimal gains of the controller. Numerical simulations are presented to verify the effectiveness of the designed controller, and the results show that the performances of the nonlinear HTRS system assisted with the proposed controller is much better than that with the commonly used optimal PID controller.

  13. Spectral risk measures: the risk quadrangle and optimal approximation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kouri, Drew P.

    We develop a general risk quadrangle that gives rise to a large class of spectral risk measures. The statistic of this new risk quadrangle is the average value-at-risk at a specific confidence level. As such, this risk quadrangle generates a continuum of error measures that can be used for superquantile regression. For risk-averse optimization, we introduce an optimal approximation of spectral risk measures using quadrature. Lastly, we prove the consistency of this approximation and demonstrate our results through numerical examples.

  14. Spectral risk measures: the risk quadrangle and optimal approximation

    DOE PAGES

    Kouri, Drew P.

    2018-05-24

    We develop a general risk quadrangle that gives rise to a large class of spectral risk measures. The statistic of this new risk quadrangle is the average value-at-risk at a specific confidence level. As such, this risk quadrangle generates a continuum of error measures that can be used for superquantile regression. For risk-averse optimization, we introduce an optimal approximation of spectral risk measures using quadrature. Lastly, we prove the consistency of this approximation and demonstrate our results through numerical examples.

  15. On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\\infty}$ Control.

    PubMed

    Wang, Ding; Mu, Chaoxu; Liu, Derong; Ma, Hongwen

    2018-04-01

    In this paper, based on the adaptive critic learning technique, the control for a class of unknown nonlinear dynamic systems is investigated by adopting a mixed data and event driven design approach. The nonlinear control problem is formulated as a two-player zero-sum differential game and the adaptive critic method is employed to cope with the data-based optimization. The novelty lies in that the data driven learning identifier is combined with the event driven design formulation, in order to develop the adaptive critic controller, thereby accomplishing the nonlinear control. The event driven optimal control law and the time driven worst case disturbance law are approximated by constructing and tuning a critic neural network. Applying the event driven feedback control, the closed-loop system is built with stability analysis. Simulation studies are conducted to verify the theoretical results and illustrate the control performance. It is significant to observe that the present research provides a new avenue of integrating data-based control and event-triggering mechanism into establishing advanced adaptive critic systems.

  16. Multidisciplinary aerospace design optimization: Survey of recent developments

    NASA Technical Reports Server (NTRS)

    Sobieszczanski-Sobieski, Jaroslaw; Haftka, Raphael T.

    1995-01-01

    The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focussed on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design-oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

  17. Airfoil Design and Optimization by the One-Shot Method

    NASA Technical Reports Server (NTRS)

    Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

    1995-01-01

    An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

  18. A robust approach to optimal matched filter design in ultrasonic non-destructive evaluation (NDE)

    NASA Astrophysics Data System (ADS)

    Li, Minghui; Hayward, Gordon

    2017-02-01

    The matched filter was demonstrated to be a powerful yet efficient technique to enhance defect detection and imaging in ultrasonic non-destructive evaluation (NDE) of coarse grain materials, provided that the filter was properly designed and optimized. In the literature, in order to accurately approximate the defect echoes, the design utilized the real excitation signals, which made it time consuming and less straightforward to implement in practice. In this paper, we present a more robust and flexible approach to optimal matched filter design using the simulated excitation signals, and the control parameters are chosen and optimized based on the real scenario of array transducer, transmitter-receiver system response, and the test sample, as a result, the filter response is optimized and depends on the material characteristics. Experiments on industrial samples are conducted and the results confirm the great benefits of the method.

  19. Airfoil optimization by the one-shot method

    NASA Technical Reports Server (NTRS)

    Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

    1994-01-01

    An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

  20. Optimizing an Actuator Array for the Control of Multi-Frequency Noise in Aircraft Interiors

    NASA Technical Reports Server (NTRS)

    Palumbo, D. L.; Padula, S. L.

    1997-01-01

    Techniques developed for selecting an optimized actuator array for interior noise reduction at a single frequency are extended to the multi-frequency case. Transfer functions for 64 actuators were obtained at 5 frequencies from ground testing the rear section of a fully trimmed DC-9 fuselage. A single loudspeaker facing the left side of the aircraft was the primary source. A combinatorial search procedure (tabu search) was employed to find optimum actuator subsets of from 2 to 16 actuators. Noise reduction predictions derived from the transfer functions were used as a basis for evaluating actuator subsets during optimization. Results indicate that it is necessary to constrain actuator forces during optimization. Unconstrained optimizations selected actuators which require unrealistically large forces. Two methods of constraint are evaluated. It is shown that a fast, but approximate, method yields results equivalent to an accurate, but computationally expensive, method.

  1. Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

    PubMed Central

    Onufriev, Alexey V.

    2013-01-01

    We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order. PMID:23861790

  2. An approximation method for configuration optimization of trusses

    NASA Technical Reports Server (NTRS)

    Hansen, Scott R.; Vanderplaats, Garret N.

    1988-01-01

    Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

  3. Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

    This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less

  4. Design of Distributed Controllers Seeking Optimal Power Flow Solutions under Communication Constraints: Preprint

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

    This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less

  5. Neural robust stabilization via event-triggering mechanism and adaptive learning technique.

    PubMed

    Wang, Ding; Liu, Derong

    2018-06-01

    The robust control synthesis of continuous-time nonlinear systems with uncertain term is investigated via event-triggering mechanism and adaptive critic learning technique. We mainly focus on combining the event-triggering mechanism with adaptive critic designs, so as to solve the nonlinear robust control problem. This can not only make better use of computation and communication resources, but also conduct controller design from the view of intelligent optimization. Through theoretical analysis, the nonlinear robust stabilization can be achieved by obtaining an event-triggered optimal control law of the nominal system with a newly defined cost function and a certain triggering condition. The adaptive critic technique is employed to facilitate the event-triggered control design, where a neural network is introduced as an approximator of the learning phase. The performance of the event-triggered robust control scheme is validated via simulation studies and comparisons. The present method extends the application domain of both event-triggered control and adaptive critic control to nonlinear systems possessing dynamical uncertainties. Copyright © 2018 Elsevier Ltd. All rights reserved.

  6. Modeling and Control of a Delayed Hepatitis B Virus Model with Incubation Period and Combination Treatment.

    PubMed

    Sun, Deshun; Liu, Fei

    2018-06-01

    In this paper, a hepatitis B virus (HBV) model with an incubation period and delayed state and control variables is firstly proposed. Furthermore, the combination treatment is adopted to have a longer-lasting effect than mono-therapy. The equilibrium points and basic reproduction number are calculated, and then the local stability is analyzed on this model. We then present optimal control strategies based on the Pontryagin's minimum principle with an objective function not only to reduce the levels of exposed cells, infected cells and free viruses nearly to zero at the end of therapy, but also to minimize the drug side-effect and the cost of treatment. What's more, we develop a numerical simulation algorithm for solving our HBV model based on the combination of forward and backward difference approximations. The state dynamics of uninfected cells, exposed cells, infected cells, free viruses, CTL and ALT are simulated with or without optimal control, which show that HBV is reduced nearly to zero based on the time-varying optimal control strategies whereas the disease would break out without control. At last, by the simulations, we prove that strategy A is the best among the three kinds of strategies we adopt and further comparisons have been done between model (1) and model (2).

  7. The role of under-determined approximations in engineering and science application

    NASA Technical Reports Server (NTRS)

    Carpenter, William C.

    1992-01-01

    There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

  8. Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form.

    PubMed

    Jagannathan, Sarangapani; He, Pingan

    2008-12-01

    In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.

  9. Strategies for global optimization in photonics design.

    PubMed

    Vukovic, Ana; Sewell, Phillip; Benson, Trevor M

    2010-10-01

    This paper reports on two important issues that arise in the context of the global optimization of photonic components where large problem spaces must be investigated. The first is the implementation of a fast simulation method and associated matrix solver for assessing particular designs and the second, the strategies that a designer can adopt to control the size of the problem design space to reduce runtimes without compromising the convergence of the global optimization tool. For this study an analytical simulation method based on Mie scattering and a fast matrix solver exploiting the fast multipole method are combined with genetic algorithms (GAs). The impact of the approximations of the simulation method on the accuracy and runtime of individual design assessments and the consequent effects on the GA are also examined. An investigation of optimization strategies for controlling the design space size is conducted on two illustrative examples, namely, 60° and 90° waveguide bends based on photonic microstructures, and their effectiveness is analyzed in terms of a GA's ability to converge to the best solution within an acceptable timeframe. Finally, the paper describes some particular optimized solutions found in the course of this work.

  10. Analysis, approximation, and computation of a coupled solid/fluid temperature control problem

    NASA Technical Reports Server (NTRS)

    Gunzburger, Max D.; Lee, Hyung C.

    1993-01-01

    An optimization problem is formulated motivated by the desire to remove temperature peaks, i.e., 'hot spots', along the bounding surfaces of containers of fluid flows. The heat equation of the solid container is coupled to the energy equations for the fluid. Heat sources can be located in the solid body, the fluid, or both. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. Both mathematical analyses and computational experiments are given.

  11. Genetic Algorithm Tuned Fuzzy Logic for Gliding Return Trajectories

    NASA Technical Reports Server (NTRS)

    Burchett, Bradley T.

    2003-01-01

    The problem of designing and flying a trajectory for successful recovery of a reusable launch vehicle is tackled using fuzzy logic control with genetic algorithm optimization. The plant is approximated by a simplified three degree of freedom non-linear model. A baseline trajectory design and guidance algorithm consisting of several Mamdani type fuzzy controllers is tuned using a simple genetic algorithm. Preliminary results show that the performance of the overall system is shown to improve with genetic algorithm tuning.

  12. Training trajectories by continuous recurrent multilayer networks.

    PubMed

    Leistritz, L; Galicki, M; Witte, H; Kochs, E

    2002-01-01

    This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagin's maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.

  13. Non-Markovian optimal sideband cooling

    NASA Astrophysics Data System (ADS)

    Triana, Johan F.; Pachon, Leonardo A.

    2018-04-01

    Optimal control theory is applied to sideband cooling of nano-mechanical resonators. The formulation described here makes use of exact results derived by means of the path-integral approach of quantum dynamics, so that no approximation is invoked. It is demonstrated that the intricate interplay between time-dependent fields and structured thermal bath may lead to improve results of the sideband cooling by an order of magnitude. Cooling is quantified by means of the mean number of phonons of the mechanical modes as well as by the von Neumann entropy. Potencial extension to non-linear systems, by means of semiclassical methods, is briefly discussed.

  14. An equivalent method for optimization of particle tuned mass damper based on experimental parametric study

    NASA Astrophysics Data System (ADS)

    Lu, Zheng; Chen, Xiaoyi; Zhou, Ying

    2018-04-01

    A particle tuned mass damper (PTMD) is a creative combination of a widely used tuned mass damper (TMD) and an efficient particle damper (PD) in the vibration control area. The performance of a one-storey steel frame attached with a PTMD is investigated through free vibration and shaking table tests. The influence of some key parameters (filling ratio of particles, auxiliary mass ratio, and particle density) on the vibration control effects is investigated, and it is shown that the attenuation level significantly depends on the filling ratio of particles. According to the experimental parametric study, some guidelines for optimization of the PTMD that mainly consider the filling ratio are proposed. Furthermore, an approximate analytical solution based on the concept of an equivalent single-particle damper is proposed, and it shows satisfied agreement between the simulation and experimental results. This simplified method is then used for the preliminary optimal design of a PTMD system, and a case study of a PTMD system attached to a five-storey steel structure following this optimization process is presented.

  15. Peak Seeking Control for Reduced Fuel Consumption with Preliminary Flight Test Results

    NASA Technical Reports Server (NTRS)

    Brown, Nelson

    2012-01-01

    The Environmentally Responsible Aviation project seeks to accomplish the simultaneous reduction of fuel burn, noise, and emissions. A project at NASA Dryden Flight Research Center is contributing to ERAs goals by exploring the practical application of real-time trim configuration optimization for enhanced performance and reduced fuel consumption. This peak-seeking control approach is based on Newton-Raphson algorithm using a time-varying Kalman filter to estimate the gradient of the performance function. In real-time operation, deflection of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of a modified F-18 are directly optimized, and the horizontal stabilators and angle of attack are indirectly optimized. Preliminary results from three research flights are presented herein. The optimization system found a trim configuration that required approximately 3.5% less fuel flow than the baseline trim at the given flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These preliminary results show the algorithm has good performance and is expected to show similar results at other flight conditions and aircraft configurations.

  16. Controlling the high frequency response of H2 by ultra-short tailored laser pulses: A time-dependent configuration interaction study

    NASA Astrophysics Data System (ADS)

    Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann

    2016-01-01

    We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H2 treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a "non-harmonic" response of H2 to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

  17. Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann, E-mail: klamroth@uni-potsdam.de

    2016-01-28

    We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show howmore » adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.« less

  18. New numerical methods for open-loop and feedback solutions to dynamic optimization problems

    NASA Astrophysics Data System (ADS)

    Ghosh, Pradipto

    The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

  19. Evaluations of the Combat Ready Clamp to Control Bleeding in Human Cadavers, Manikins, Swine Femoral Artery Hemorrhage Model and Swine Carcasses

    DTIC Science & Technology

    2012-06-01

    some advantages over alternative live tissue models when a mechanical device is employed to reduce arterial flow rates. Authentic human anatomy is...vessels to reduce and stop blood flow require authentic human anatomy for optimal testing. Cadaver I was approximately 60 year old male with a total

  20. Geometry of Quantum Computation with Qudits

    PubMed Central

    Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

    2014-01-01

    The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

  1. Multidisciplinary Design Optimization for Aeropropulsion Engines and Solid Modeling/Animation via the Integrated Forced Methods

    NASA Technical Reports Server (NTRS)

    2004-01-01

    The grant closure report is organized in the following four chapters: Chapter describes the two research areas Design optimization and Solid mechanics. Ten journal publications are listed in the second chapter. Five highlights is the subject matter of chapter three. CHAPTER 1. The Design Optimization Test Bed CometBoards. CHAPTER 2. Solid Mechanics: Integrated Force Method of Analysis. CHAPTER 3. Five Highlights: Neural Network and Regression Methods Demonstrated in the Design Optimization of a Subsonic Aircraft. Neural Network and Regression Soft Model Extended for PX-300 Aircraft Engine. Engine with Regression and Neural Network Approximators Designed. Cascade Optimization Strategy with Neural network and Regression Approximations Demonstrated on a Preliminary Aircraft Engine Design. Neural Network and Regression Approximations Used in Aircraft Design.

  2. Tool Support for Software Lookup Table Optimization

    DOE PAGES

    Wilcox, Chris; Strout, Michelle Mills; Bieman, James M.

    2011-01-01

    A number of scientific applications are performance-limited by expressions that repeatedly call costly elementary functions. Lookup table (LUT) optimization accelerates the evaluation of such functions by reusing previously computed results. LUT methods can speed up applications that tolerate an approximation of function results, thereby achieving a high level of fuzzy reuse. One problem with LUT optimization is the difficulty of controlling the tradeoff between performance and accuracy. The current practice of manual LUT optimization adds programming effort by requiring extensive experimentation to make this tradeoff, and such hand tuning can obfuscate algorithms. In this paper we describe a methodology andmore » tool implementation to improve the application of software LUT optimization. Our Mesa tool implements source-to-source transformations for C or C++ code to automate the tedious and error-prone aspects of LUT generation such as domain profiling, error analysis, and code generation. We evaluate Mesa with five scientific applications. Our results show a performance improvement of 3.0× and 6.9× for two molecular biology algorithms, 1.4× for a molecular dynamics program, 2.1× to 2.8× for a neural network application, and 4.6× for a hydrology calculation. We find that Mesa enables LUT optimization with more control over accuracy and less effort than manual approaches.« less

  3. Solving bi-level optimization problems in engineering design using kriging models

    NASA Astrophysics Data System (ADS)

    Xia, Yi; Liu, Xiaojie; Du, Gang

    2018-05-01

    Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.

  4. Identifying Cost-Effective Dynamic Policies to Control Epidemics

    PubMed Central

    Yaesoubi, Reza; Cohen, Ted

    2016-01-01

    We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population’s net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. PMID:27449759

  5. Convex optimisation approach to constrained fuel optimal control of spacecraft in close relative motion

    NASA Astrophysics Data System (ADS)

    Massioni, Paolo; Massari, Mauro

    2018-05-01

    This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.

  6. Design and evaluation of a Stochastic Optimal Feed-forward and Feedback Technology (SOFFT) flight control architecture

    NASA Technical Reports Server (NTRS)

    Ostroff, Aaron J.; Proffitt, Melissa S.

    1994-01-01

    This paper describes the design and evaluation of a stochastic optimal feed-forward and feedback technology (SOFFT) control architecture with emphasis on the feed-forward controller design. The SOFFT approach allows the designer to independently design the feed-forward and feedback controllers to meet separate objectives and then integrate the two controllers. The feed-forward controller has been integrated with an existing high-angle-of-attack (high-alpha) feedback controller. The feed-forward controller includes a variable command model with parameters selected to satisfy level 1 flying qualities with a high-alpha adjustment to achieve desired agility guidelines, a nonlinear interpolation approach that scales entire matrices for approximation of the plant model, and equations for calculating feed-forward gains developed for perfect plant-model tracking. The SOFFT design was applied to a nonlinear batch simulation model of an F/A-18 aircraft modified for thrust vectoring. Simulation results show that agility guidelines are met and that the SOFFT controller filters undesired pilot-induced frequencies more effectively during a tracking task than a flight controller that has the same feedback control law but does not have the SOFFT feed-forward control.

  7. Numerical Investigations of an Optimized Airfoil with a Rotary Cylinder

    NASA Astrophysics Data System (ADS)

    Gada, Komal; Rahai, Hamid

    2015-11-01

    Numerical Investigations of an optimized thin airfoil with a rotary cylinder as a control device for reducing separation and improving lift to drag ratio have been performed. Our previous investigations have used geometrical optimization for development of an optimized airfoil with increased torque for applications in a vertical axis wind turbine. The improved performance was due to contributions of lift to torque at low angles of attack. The current investigations have been focused on using the optimized airfoil for micro-uav applications with an active flow control device, a rotary cylinder, to further control flow separation, especially during wind gust conditions. The airfoil has a chord length of 19.66 cm and a width of 25 cm with 0.254 cm thickness. Previous investigations have shown flow separation at approximately 85% chord length at moderate angles of attack. Thus the rotary cylinder with a 0.254 cm diameter was placed slightly downstream of the location of flow separation. The free stream mean velocity was 10 m/sec. and investigations have been performed at different cylinder's rotations with corresponding tangential velocities higher than, equal to and less than the free stream velocity. Results have shown more than 10% improvement in lift to drag ratio when the tangential velocity is near the free stream mean velocity. Graduate Assistant, Center for Energy and Environmental Research and Services (CEERS), College of Engineering, California State University, Long Beach.

  8. Methodology for determination and use of the no-escape envelope of an air-to-air-missile

    NASA Technical Reports Server (NTRS)

    Neuman, Frank

    1988-01-01

    A large gap exists between optimal control and differential-game theory and their applications. The purpose of this paper is to show how this gap may be bridged. Missile-avoidance of realistically simulated infrared heat-seeking, fire-and-forget missile is studied. In detailed simulations, sweeping out the discretized initial condition space, avoidance methods based on pilot experience are combined with those based on simplified optimal control analysis to derive an approximation to the no-escape missile envelopes. The detailed missile equations and no-escape envelopes were then incorporated into an existing piloted simulation of air-to-air combat to generate missile firing decisions as well as missile avoidance commands. The use of these envelopes was found to be effective in both functions.

  9. Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

    NASA Technical Reports Server (NTRS)

    Putko, Michele M.; Taylor, Arthur C., III; Newman, Perry A.; Green, Lawrence L.

    2002-01-01

    An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

  10. DQE and system optimization for indirect-detection flat-panel imagers in diagnostic radiology

    NASA Astrophysics Data System (ADS)

    Siewerdsen, Jeffrey H.; Antonuk, Larry E.

    1998-07-01

    The performance of indirect-detection flat-panel imagers incorporating CsI:Tl x-ray converters is examined through calculation of the detective quantum efficiency (DQE) under conditions of chest radiography, fluoroscopy, and mammography. Calculations are based upon a cascaded systems model which has demonstrated excellent agreement with empirical signal, noise- power spectra, and DQE results. For each application, the DQE is calculated as a function of spatial-frequency and CsI:Tl thickness. A preliminary investigation into the optimization of flat-panel imaging systems is described, wherein the x-ray converter thickness which provides optimal DQE for a given imaging task is estimated. For each application, a number of example tasks involving detection of an object of variable size and contrast against a noisy background are considered. The method described is fairly general and can be extended to account for a variety of imaging tasks. For the specific examples considered, the preliminary results estimate optimal CsI:Tl thicknesses of approximately 450 micrometer (approximately 200 mg/cm2), approximately 320 micrometer (approximately 140 mg/cm2), and approximately 200 micrometer (approximately 90 mg/cm2) for chest radiography, fluoroscopy, and mammography, respectively. These results are expected to depend upon the imaging task as well as upon the quality of available CsI:Tl, and future improvements in scintillator fabrication could result in increased optimal thickness and DQE.

  11. Singular perturbation analysis of AOTV-related trajectory optimization problems

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Bae, Gyoung H.

    1990-01-01

    The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

  12. Exponential approximations in optimal design

    NASA Technical Reports Server (NTRS)

    Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

    1990-01-01

    One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

  13. Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

    NASA Technical Reports Server (NTRS)

    Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

    2016-01-01

    A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

  14. Optimizing Controlling-Value-Based Power Gating with Gate Count and Switching Activity

    NASA Astrophysics Data System (ADS)

    Chen, Lei; Kimura, Shinji

    In this paper, a new heuristic algorithm is proposed to optimize the power domain clustering in controlling-value-based (CV-based) power gating technology. In this algorithm, both the switching activity of sleep signals (p) and the overall numbers of sleep gates (gate count, N) are considered, and the sum of the product of p and N is optimized. The algorithm effectively exerts the total power reduction obtained from the CV-based power gating. Even when the maximum depth is kept to be the same, the proposed algorithm can still achieve power reduction approximately 10% more than that of the prior algorithms. Furthermore, detailed comparison between the proposed heuristic algorithm and other possible heuristic algorithms are also presented. HSPICE simulation results show that over 26% of total power reduction can be obtained by using the new heuristic algorithm. In addition, the effect of dynamic power reduction through the CV-based power gating method and the delay overhead caused by the switching of sleep transistors are also shown in this paper.

  15. Techniques for designing rotorcraft control systems

    NASA Technical Reports Server (NTRS)

    Levine, William S.; Barlow, Jewel

    1993-01-01

    This report summarizes the work that was done on the project from 1 Apr. 1992 to 31 Mar. 1993. The main goal of this research is to develop a practical tool for rotorcraft control system design based on interactive optimization tools (CONSOL-OPTCAD) and classical rotorcraft design considerations (ADOCS). This approach enables the designer to combine engineering intuition and experience with parametric optimization. The combination should make it possible to produce a better design faster than would be possible using either pure optimization or pure intuition and experience. We emphasize that the goal of this project is not to develop an algorithm. It is to develop a tool. We want to keep the human designer in the design process to take advantage of his or her experience and creativity. The role of the computer is to perform the calculation necessary to improve and to display the performance of the nominal design. Briefly, during the first year we have connected CONSOL-OPTCAD, an existing software package for optimizing parameters with respect to multiple performance criteria, to a simplified nonlinear simulation of the UH-60 rotorcraft. We have also created mathematical approximations to the Mil-specs for rotorcraft handling qualities and input them into CONSOL-OPTCAD. Finally, we have developed the additional software necessary to use CONSOL-OPTCAD for the design of rotorcraft controllers.

  16. Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

    NASA Astrophysics Data System (ADS)

    Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

    2017-08-01

    Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

  17. Efficient algorithms for a class of partitioning problems

    NASA Technical Reports Server (NTRS)

    Iqbal, M. Ashraf; Bokhari, Shahid H.

    1990-01-01

    The problem of optimally partitioning the modules of chain- or tree-like tasks over chain-structured or host-satellite multiple computer systems is addressed. This important class of problems includes many signal processing and industrial control applications. Prior research has resulted in a succession of faster exact and approximate algorithms for these problems. Polynomial exact and approximate algorithms are described for this class that are better than any of the previously reported algorithms. The approach is based on a preprocessing step that condenses the given chain or tree structured task into a monotonic chain or tree. The partitioning of this monotonic take can then be carried out using fast search techniques.

  18. Batch Mode Reinforcement Learning based on the Synthesis of Artificial Trajectories

    PubMed Central

    Fonteneau, Raphael; Murphy, Susan A.; Wehenkel, Louis; Ernst, Damien

    2013-01-01

    In this paper, we consider the batch mode reinforcement learning setting, where the central problem is to learn from a sample of trajectories a policy that satisfies or optimizes a performance criterion. We focus on the continuous state space case for which usual resolution schemes rely on function approximators either to represent the underlying control problem or to represent its value function. As an alternative to the use of function approximators, we rely on the synthesis of “artificial trajectories” from the given sample of trajectories, and show that this idea opens new avenues for designing and analyzing algorithms for batch mode reinforcement learning. PMID:24049244

  19. On optimal strategies in event-constrained differential games

    NASA Technical Reports Server (NTRS)

    Heymann, M.; Rajan, N.; Ardema, M.

    1985-01-01

    Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.

  20. Methods of Constructing a Blended Performance Function Suitable for Formation Flight

    NASA Technical Reports Server (NTRS)

    Ryan, Jack

    2017-01-01

    Two methods for constructing performance functions for formation fight-for-drag-reduction suitable for use with an extreme-seeking control system are presented. The first method approximates an a prior measured or estimated drag-reduction performance function by combining real-time measurements of readily available parameters. The parameters are combined with weightings determined from a minimum squares optimization to form a blended performance function.

  1. The performance of a reduced-order adaptive controller when used in multi-antenna hyperthermia treatments with nonlinear temperature-dependent perfusion.

    PubMed

    Cheng, Kung-Shan; Yuan, Yu; Li, Zhen; Stauffer, Paul R; Maccarini, Paolo; Joines, William T; Dewhirst, Mark W; Das, Shiva K

    2009-04-07

    In large multi-antenna systems, adaptive controllers can aid in steering the heat focus toward the tumor. However, the large number of sources can greatly increase the steering time. Additionally, controller performance can be degraded due to changes in tissue perfusion which vary non-linearly with temperature, as well as with time and spatial position. The current work investigates whether a reduced-order controller with the assumption of piecewise constant perfusion is robust to temperature-dependent perfusion and achieves steering in a shorter time than required by a full-order controller. The reduced-order controller assumes that the optimal heating setting lies in a subspace spanned by the best heating vectors (virtual sources) of an initial, approximate, patient model. An initial, approximate, reduced-order model is iteratively updated by the controller, using feedback thermal images, until convergence of the heat focus to the tumor. Numerical tests were conducted in a patient model with a right lower leg sarcoma, heated in a 10-antenna cylindrical mini-annual phased array applicator operating at 150 MHz. A half-Gaussian model was used to simulate temperature-dependent perfusion. Simulated magnetic resonance temperature images were used as feedback at each iteration step. Robustness was validated for the controller, starting from four approximate initial models: (1) a 'standard' constant perfusion lower leg model ('standard' implies a model that exactly models the patient with the exception that perfusion is considered constant, i.e., not temperature dependent), (2) a model with electrical and thermal tissue properties varied from 50% higher to 50% lower than the standard model, (3) a simplified constant perfusion pure-muscle lower leg model with +/-50% deviated properties and (4) a standard model with the tumor position in the leg shifted by 1.5 cm. Convergence to the desired focus of heating in the tumor was achieved for all four simulated models. The controller accomplished satisfactory therapeutic outcomes: approximately 80% of the tumor was heated to temperatures 43 degrees C and approximately 93% was maintained at temperatures <41 degrees C. Compared to the controller without model reduction, a approximately 9-25 fold reduction in convergence time was accomplished using approximately 2-3 orthonormal virtual sources. In the situations tested, the controller was robust to the presence of temperature-dependent perfusion. The results of this work can help to lay the foundation for real-time thermal control of multi-antenna hyperthermia systems in clinical situations where perfusion can change rapidly with temperature.

  2. Statistical optimization of beta-carotene production by Arthrobacter agilis A17 using response surface methodology and Box-Behnken design

    NASA Astrophysics Data System (ADS)

    Özdal, Murat; Özdal, Özlem Gür; Gürkök, Sümeyra

    2017-04-01

    β-carotene is a commercially important natural pigment and has been widely applied in the medicine, pharmaceutical, food, feed and cosmetic industries. The current study aimed to investigate the usability of molasses for β-carotene production by Arthrobacter agilis A17 (KP318146) and to optimize the production process. Box-Behnken Design of Response Surface Methodology was used to determine the optimum levels and the interactions of three independent variables namely molasses, yeast extract and KH2PO4 at three different levels. β-carotene yield in optimized medium containing 70 g/l molasses, 25 g/l yeast extract and 0.96 g/l KH2PO4, reached up to 100 mg/l, which is approximately 2.5-fold higher than the yield, obtained from control cultivation. A remarkable β-carotene production on inexpensive carbon source was achieved with the use of statistical optimization.

  3. A trust region-based approach to optimize triple response systems

    NASA Astrophysics Data System (ADS)

    Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

    2014-05-01

    This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

  4. Implementing of lognormal humidity and cloud-related control variables for the NCEP GSI hybrid EnVAR Assimilation scheme.

    NASA Astrophysics Data System (ADS)

    Fletcher, S. J.; Kleist, D.; Ide, K.

    2017-12-01

    As the resolution of operational global numerical weather prediction system approach the meso-scale, then the assumption of Gaussianity for the errors at these scales may not valid. However, it is also true that synoptic variables that are positive definite in behavior, for example humidity, cannot be optimally analyzed with a Gaussian error structure, where the increment could force the full field to go negative. In this presentation we present the initial work of implementing a mixed Gaussian-lognormal approximation for the temperature and moisture variable in both the ensemble and variational component of the NCEP GSI hybrid EnVAR. We shall also lay the foundation for the implementation of the lognormal approximation to cloud related control variables to allow for a possible more consistent assimilation of cloudy radiances.

  5. Realization of the three-qubit quantum controlled gate based on matching Hermitian generators

    NASA Astrophysics Data System (ADS)

    Gautam, Kumar; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet; Upadhyaya, Varun

    2017-05-01

    This paper deals with the design of quantum unitary gate by matching the Hermitian generators. A given complicated quantum controlled gate is approximated by perturbing a simple quantum system with a small time-varying potential. The basic idea is to evaluate the generator H_φ of the perturbed system approximately using first-order perturbation theory in the interaction picture. H_φ depends on a modulating signal φ(t){:} 0≤t≤T which modulates a known potential V. The generator H_φ of the given gate U_g is evaluated using H_g=ι log U_g. The optimal modulating signal φ(t) is chosen so that \\Vert H_g - H_φ \\Vert is a minimum. The simple quantum system chosen for our simulation is harmonic oscillator with charge perturbed by an electric field that is a constant in space but time varying and is controlled externally. This is used to approximate the controlled unitary gate obtained by perturbing the oscillator with an anharmonic term proportional to q^3. Simulations results show significantly small noise-to-signal ratio. Finally, we discuss how the proposed method is particularly suitable for designing some commonly used unitary gates. Another example was chosen to illustrate this method of gate design is the ion-trap model.

  6. Robust approximate optimal guidance strategies for aeroassisted orbital transfer missions

    NASA Astrophysics Data System (ADS)

    Ilgen, Marc R.

    This thesis presents the application of game theoretic and regular perturbation methods to the problem of determining robust approximate optimal guidance laws for aeroassisted orbital transfer missions with atmospheric density and navigated state uncertainties. The optimal guidance problem is reformulated as a differential game problem with the guidance law designer and Nature as opposing players. The resulting equations comprise the necessary conditions for the optimal closed loop guidance strategy in the presence of worst case parameter variations. While these equations are nonlinear and cannot be solved analytically, the presence of a small parameter in the equations of motion allows the method of regular perturbations to be used to solve the equations approximately. This thesis is divided into five parts. The first part introduces the class of problems to be considered and presents results of previous research. The second part then presents explicit semianalytical guidance law techniques for the aerodynamically dominated region of flight. These guidance techniques are applied to unconstrained and control constrained aeroassisted plane change missions and Mars aerocapture missions, all subject to significant atmospheric density variations. The third part presents a guidance technique for aeroassisted orbital transfer problems in the gravitationally dominated region of flight. Regular perturbations are used to design an implicit guidance technique similar to the second variation technique but that removes the need for numerically computing an optimal trajectory prior to flight. This methodology is then applied to a set of aeroassisted inclination change missions. In the fourth part, the explicit regular perturbation solution technique is extended to include the class of guidance laws with partial state information. This methodology is then applied to an aeroassisted plane change mission using inertial measurements and subject to uncertainties in the initial value of the flight path angle. A summary of performance results for all these guidance laws is presented in the fifth part of this thesis along with recommendations for further research.

  7. Optimal feedback control of turbulent channel flow

    NASA Technical Reports Server (NTRS)

    Bewley, Thomas; Choi, Haecheon; Temam, Roger; Moin, Parviz

    1993-01-01

    Feedback control equations were developed and tested for computing wall normal control velocities to control turbulent flow in a channel with the objective of reducing drag. The technique used is the minimization of a 'cost functional' which is constructed to represent some balance of the drag integrated over the wall and the net control effort. A distribution of wall velocities is found which minimizes this cost functional some time shortly in the future based on current observations of the flow near the wall. Preliminary direct numerical simulations of the scheme applied to turbulent channel flow indicates it provides approximately 17 percent drag reduction. The mechanism apparent when the scheme is applied to a simplified flow situation is also discussed.

  8. Dynamic programming methods for concurrent design and dynamic allocation of vehicles embedded in a system-of-systems

    NASA Astrophysics Data System (ADS)

    Nusawardhana

    2007-12-01

    Recent developments indicate a changing perspective on how systems or vehicles should be designed. Such transition comes from the way decision makers in defense related agencies address complex problems. Complex problems are now often posed in terms of the capabilities desired, rather than in terms of requirements for a single systems. As a result, the way to provide a set of capabilities is through a collection of several individual, independent systems. This collection of individual independent systems is often referred to as a "System of Systems'' (SoS). Because of the independent nature of the constituent systems in an SoS, approaches to design an SoS, and more specifically, approaches to design a new system as a member of an SoS, will likely be different than the traditional design approaches for complex, monolithic (meaning the constituent parts have no ability for independent operation) systems. Because a system of system evolves over time, this simultaneous system design and resource allocation problem should be investigated in a dynamic context. Such dynamic optimization problems are similar to conventional control problems. However, this research considers problems which not only seek optimizing policies but also seek the proper system or vehicle to operate under these policies. This thesis presents a framework and a set of analytical tools to solve a class of SoS problems that involves the simultaneous design of a new system and allocation of the new system along with existing systems. Such a class of problems belongs to the problems of concurrent design and control of a new systems with solutions consisting of both optimal system design and optimal control strategy. Rigorous mathematical arguments show that the proposed framework solves the concurrent design and control problems. Many results exist for dynamic optimization problems of linear systems. In contrary, results on optimal nonlinear dynamic optimization problems are rare. The proposed framework is equipped with the set of analytical tools to solve several cases of nonlinear optimal control problems: continuous- and discrete-time nonlinear problems with applications on both optimal regulation and tracking. These tools are useful when mathematical descriptions of dynamic systems are available. In the absence of such a mathematical model, it is often necessary to derive a solution based on computer simulation. For this case, a set of parameterized decision may constitute a solution. This thesis presents a method to adjust these parameters based on the principle of stochastic approximation simultaneous perturbation using continuous measurements. The set of tools developed here mostly employs the methods of exact dynamic programming. However, due to the complexity of SoS problems, this research also develops suboptimal solution approaches, collectively recognized as approximate dynamic programming solutions, for large scale problems. The thesis presents, explores, and solves problems from an airline industry, in which a new aircraft is to be designed and allocated along with an existing fleet of aircraft. Because the life cycle of an aircraft is on the order of 10 to 20 years, this problem is to be addressed dynamically so that the new aircraft design is the best design for the fleet over a given time horizon.

  9. Optimization and Control of Agent-Based Models in Biology: A Perspective.

    PubMed

    An, G; Fitzpatrick, B G; Christley, S; Federico, P; Kanarek, A; Neilan, R Miller; Oremland, M; Salinas, R; Laubenbacher, R; Lenhart, S

    2017-01-01

    Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

  10. Vibroacoustic optimization using a statistical energy analysis model

    NASA Astrophysics Data System (ADS)

    Culla, Antonio; D`Ambrogio, Walter; Fregolent, Annalisa; Milana, Silvia

    2016-08-01

    In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF) and coupling loss factors (CLF), which in turn depend on the physical parameters of the subsystems. A preliminary sensitivity analysis of subsystem energy to CLF's is performed to select CLF's that are most effective on subsystem energies. Since the injected power depends not only on the external loads but on the physical parameters of the subsystems as well, it must be taken into account under certain conditions. This is accomplished in the optimization procedure, where approximate relationships between CLF's, injected power and physical parameters are derived. The approach is applied on a typical aeronautical structure: the cabin of a helicopter.

  11. Broken symmetry in a two-qubit quantum control landscape

    NASA Astrophysics Data System (ADS)

    Bukov, Marin; Day, Alexandre G. R.; Weinberg, Phillip; Polkovnikov, Anatoli; Mehta, Pankaj; Sels, Dries

    2018-05-01

    We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a spontaneous breaking of a Z2 symmetry in the functional form of the optimal protocol, and occurs below the quantum speed limit. We study in detail this phase and demonstrate that even though high-fidelity protocols come degenerate with respect to their fidelity, they lead to final states of different entanglement entropy shared between the qubits. Consequently, while globally both optimal protocols are equally far away from the target state, one is locally closer than the other. An approximate variational mean-field theory which captures the physics of the different phases is developed.

  12. Global optimization method based on ray tracing to achieve optimum figure error compensation

    NASA Astrophysics Data System (ADS)

    Liu, Xiaolin; Guo, Xuejia; Tang, Tianjin

    2017-02-01

    Figure error would degrade the performance of optical system. When predicting the performance and performing system assembly, compensation by clocking of optical components around the optical axis is a conventional but user-dependent method. Commercial optical software cannot optimize this clocking. Meanwhile existing automatic figure-error balancing methods can introduce approximate calculation error and the build process of optimization model is complex and time-consuming. To overcome these limitations, an accurate and automatic global optimization method of figure error balancing is proposed. This method is based on precise ray tracing to calculate the wavefront error, not approximate calculation, under a given elements' rotation angles combination. The composite wavefront error root-mean-square (RMS) acts as the cost function. Simulated annealing algorithm is used to seek the optimal combination of rotation angles of each optical element. This method can be applied to all rotational symmetric optics. Optimization results show that this method is 49% better than previous approximate analytical method.

  13. Inverse Diffusion Curves Using Shape Optimization.

    PubMed

    Zhao, Shuang; Durand, Fredo; Zheng, Changxi

    2018-07-01

    The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

  14. Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Duckeman, Gregory A.

    1994-01-01

    In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

  15. Fast approximation for joint optimization of segmentation, shape, and location priors, and its application in gallbladder segmentation.

    PubMed

    Saito, Atsushi; Nawano, Shigeru; Shimizu, Akinobu

    2017-05-01

    This paper addresses joint optimization for segmentation and shape priors, including translation, to overcome inter-subject variability in the location of an organ. Because a simple extension of the previous exact optimization method is too computationally complex, we propose a fast approximation for optimization. The effectiveness of the proposed approximation is validated in the context of gallbladder segmentation from a non-contrast computed tomography (CT) volume. After spatial standardization and estimation of the posterior probability of the target organ, simultaneous optimization of the segmentation, shape, and location priors is performed using a branch-and-bound method. Fast approximation is achieved by combining sampling in the eigenshape space to reduce the number of shape priors and an efficient computational technique for evaluating the lower bound. Performance was evaluated using threefold cross-validation of 27 CT volumes. Optimization in terms of translation of the shape prior significantly improved segmentation performance. The proposed method achieved a result of 0.623 on the Jaccard index in gallbladder segmentation, which is comparable to that of state-of-the-art methods. The computational efficiency of the algorithm is confirmed to be good enough to allow execution on a personal computer. Joint optimization of the segmentation, shape, and location priors was proposed, and it proved to be effective in gallbladder segmentation with high computational efficiency.

  16. Aerospace plane guidance using geometric control theory

    NASA Technical Reports Server (NTRS)

    Van Buren, Mark A.; Mease, Kenneth D.

    1990-01-01

    A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.

  17. Optimal control of build height utilizing optical profilometry in cold spray deposits

    NASA Astrophysics Data System (ADS)

    Chakraborty, Abhijit; Shishkin, Sergey; Birnkrant, Michael J.

    2017-04-01

    Part-to-part variability and poor part quality due to failure to maintain geometric specifications pose a challenge for adopting Additive Manufacturing (AM) as a viable manufacturing process. In recent years, In-process Monitoring and Control (InPMC) has received a lot of attention as an approach to overcome these obstacles. The ability to sense geometry of the deposited layers accurately enables effective process monitoring and control of AM application. This paper demonstrates an application of geometry sensing technique for the coating deposition Cold Spray process, where solid powders are accelerated through a nozzle, collides with the substrate and adheres to it. Often the deposited surface has shape irregularities. This paper proposes an approach to suppress the iregularities by controlling the deposition height. An analytical control-oriented model is developed that expresses the resulting height of deposit as an integral function of nozzle velocity and angle. In order to obtain height information at each layer, a Micro-Epsilon laser line scanner was used for surface profiling after each deposition. This surface profile information, specifically the layer height, was then fed back to an optimal control algorithm which manipulated the nozzle speed to control the layer height to a pre specified height. While the problem is heavily nonlinear, we were able to transform it into equivalent Optimal Control problem linear w.r.t. input. That enabled development of two solution methods: one is fast and approximate, while another is more accurate but still efficient.

  18. Contributions on Optimizing Approximations in the Study of Melting and Solidification Processes That Occur in Processing by Electro-Erosion

    NASA Astrophysics Data System (ADS)

    Potra, F. L.; Potra, T.; Soporan, V. F.

    We propose two optimization methods of the processes which appear in EDM (Electrical Discharge Machining). First refers to the introduction of a new function approximating the thermal flux energy in EDM machine. Classical researches approximate this energy with the Gauss' function. In the case of unconventional technology the Gauss' bell became null only for r → +∞, where r is the radius of crater produced by EDM. We introduce a cubic spline regression which descends to zero at the crater's boundary. In the second optimization we propose modifications in technologies' work regarding the displacement of the tool electrode to the piece electrode such that the material melting to be realized in optimal time and the feeding speed with dielectric liquid regarding the solidification of the expulsed material. This we realize using the FAHP algorithm based on the theory of eigenvalues and eigenvectors, which lead to mean values of best approximation. [6

  19. Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

    NASA Technical Reports Server (NTRS)

    Putko, Michele M.; Newman, Perry A.; Taylor, Arthur C., III; Green, Lawrence L.

    2001-01-01

    This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

  20. Solving the infeasible trust-region problem using approximations.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Renaud, John E.; Perez, Victor M.; Eldred, Michael Scott

    2004-07-01

    The use of optimization in engineering design has fueled the development of algorithms for specific engineering needs. When the simulations are expensive to evaluate or the outputs present some noise, the direct use of nonlinear optimizers is not advisable, since the optimization process will be expensive and may result in premature convergence. The use of approximations for both cases is an alternative investigated by many researchers including the authors. When approximations are present, a model management is required for proper convergence of the algorithm. In nonlinear programming, the use of trust-regions for globalization of a local algorithm has been provenmore » effective. The same approach has been used to manage the local move limits in sequential approximate optimization frameworks as in Alexandrov et al., Giunta and Eldred, Perez et al. , Rodriguez et al., etc. The experience in the mathematical community has shown that more effective algorithms can be obtained by the specific inclusion of the constraints (SQP type of algorithms) rather than by using a penalty function as in the augmented Lagrangian formulation. The presence of explicit constraints in the local problem bounded by the trust region, however, may have no feasible solution. In order to remedy this problem the mathematical community has developed different versions of a composite steps approach. This approach consists of a normal step to reduce the amount of constraint violation and a tangential step to minimize the objective function maintaining the level of constraint violation attained at the normal step. Two of the authors have developed a different approach for a sequential approximate optimization framework using homotopy ideas to relax the constraints. This algorithm called interior-point trust-region sequential approximate optimization (IPTRSAO) presents some similarities to the two normal-tangential steps algorithms. In this paper, a description of the similarities is presented and an expansion of the two steps algorithm is presented for the case of approximations.« less

  1. Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi

    1990-01-01

    In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

  2. Improving the Critic Learning for Event-Based Nonlinear $H_{\\infty }$ Control Design.

    PubMed

    Wang, Ding; He, Haibo; Liu, Derong

    2017-10-01

    In this paper, we aim at improving the critic learning criterion to cope with the event-based nonlinear H ∞ state feedback control design. First of all, the H ∞ control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal intersample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.

  3. Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

    NASA Technical Reports Server (NTRS)

    Tiffany, Sherwood H.; Adams, William M., Jr.

    1987-01-01

    This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

  4. Using spatial information about recurrence risk for robust optimization of dose-painting prescription functions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bender, Edward T.

    Purpose: To develop a robust method for deriving dose-painting prescription functions using spatial information about the risk for disease recurrence. Methods: Spatial distributions of radiobiological model parameters are derived from distributions of recurrence risk after uniform irradiation. These model parameters are then used to derive optimal dose-painting prescription functions given a constant mean biologically effective dose. Results: An estimate for the optimal dose distribution can be derived based on spatial information about recurrence risk. Dose painting based on imaging markers that are moderately or poorly correlated with recurrence risk are predicted to potentially result in inferior disease control when comparedmore » the same mean biologically effective dose delivered uniformly. A robust optimization approach may partially mitigate this issue. Conclusions: The methods described here can be used to derive an estimate for a robust, patient-specific prescription function for use in dose painting. Two approximate scaling relationships were observed: First, the optimal choice for the maximum dose differential when using either a linear or two-compartment prescription function is proportional to R, where R is the Pearson correlation coefficient between a given imaging marker and recurrence risk after uniform irradiation. Second, the predicted maximum possible gain in tumor control probability for any robust optimization technique is nearly proportional to the square of R.« less

  5. WavePacket: A Matlab package for numerical quantum dynamics.II: Open quantum systems, optimal control, and model reduction

    NASA Astrophysics Data System (ADS)

    Schmidt, Burkhard; Hartmann, Carsten

    2018-07-01

    WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm. The present work describes the MATLAB version of WavePacket 5.3.0 which is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics can be found.

  6. Combined design of structures and controllers for optimal maneuverability

    NASA Technical Reports Server (NTRS)

    Ling, Jer; Kabamba, Pierre; Taylor, John

    1990-01-01

    Approaches to the combined design of structures and controllers for achieving optimal maneuverability are presented. A maneuverability index which directly reflects the minimum time required to perform a given set of maneuvers is introduced. By designing the flexible appendages, the maneuver time of the spacecraft is minimized under the constraints of structural properties, and post maneuver spillover is kept within a specified bound. The spillover reduction is achieved by making use of an appropriate reduced order model. The distributed parameter design problem is approached using assumed shape functions, and finite element analysis with dynamic reduction. Solution procedures have been investigated. Approximate design methods have been developed to overcome the computational difficulties. Some new constraints on the modal frequencies of the spacecraft are introduced in the original optimization problem to facilitate the solution process. It is shown that the global optimal design may be obtained by tuning the natural frequencies to satisfy specific constraints. Researchers quantify the difference between a lower bound to the solution for maneuver time associated with the original problem and the estimate obtained from the modified problem, for a specified application requirement. Numerical examples are presented to demonstrate the capability of this approach.

  7. An alternative laser driven photodissociation mechanism of pyrrole via πσ*1∕S0 conical intersection.

    PubMed

    Nandipati, K R; Lan, Z; Singh, H; Mahapatra, S

    2017-06-07

    A first principles quantum dynamics study of N-H photodissociation of pyrrole on the S 0 - 1 πσ * (A21) coupled electronic states is carried out with the aid of an optimally designed UV-laser pulse. A new photodissociation path, as compared to the conventional barrier crossing on the πσ*1 state, opens up upon electronic transitions under the influence of pump-dump laser pulses, which efficiently populate both the dissociation channels. The interplay of electronic transitions due both to vibronic coupling and the laser pulse is observed in the control mechanism and discussed in detail. The proposed control mechanism seems to be robust, and not discussed in the literature so far, and is expected to trigger future experiments on the πσ*1 photochemistry of molecules of chemical and biological importance. The design of the optimal pulses and their application to enhance the overall dissociation probability is carried out within the framework of optimal control theory. The quantum dynamics of the system in the presence of pulse is treated by solving the time-dependent Schrödinger equation in the semi-classical dipole approximation.

  8. An alternative laser driven photodissociation mechanism of pyrrole via πσ*1∕S0 conical intersection

    PubMed Central

    Nandipati, K. R.; Lan, Z.; Singh, H.; Mahapatra, S.

    2017-01-01

    A first principles quantum dynamics study of N–H photodissociation of pyrrole on the S0−1πσ*(A21) coupled electronic states is carried out with the aid of an optimally designed UV-laser pulse. A new photodissociation path, as compared to the conventional barrier crossing on the πσ*1 state, opens up upon electronic transitions under the influence of pump-dump laser pulses, which efficiently populate both the dissociation channels. The interplay of electronic transitions due both to vibronic coupling and the laser pulse is observed in the control mechanism and discussed in detail. The proposed control mechanism seems to be robust, and not discussed in the literature so far, and is expected to trigger future experiments on the πσ*1 photochemistry of molecules of chemical and biological importance. The design of the optimal pulses and their application to enhance the overall dissociation probability is carried out within the framework of optimal control theory. The quantum dynamics of the system in the presence of pulse is treated by solving the time-dependent Schrödinger equation in the semi-classical dipole approximation. PMID:28595406

  9. An alternative laser driven photodissociation mechanism of pyrrole via π*1σ/S0 conical intersection

    NASA Astrophysics Data System (ADS)

    Nandipati, K. R.; Lan, Z.; Singh, H.; Mahapatra, S.

    2017-06-01

    A first principles quantum dynamics study of N-H photodissociation of pyrrole on the S0-1π σ*(A12) coupled electronic states is carried out with the aid of an optimally designed UV-laser pulse. A new photodissociation path, as compared to the conventional barrier crossing on the π*1σ state, opens up upon electronic transitions under the influence of pump-dump laser pulses, which efficiently populate both the dissociation channels. The interplay of electronic transitions due both to vibronic coupling and the laser pulse is observed in the control mechanism and discussed in detail. The proposed control mechanism seems to be robust, and not discussed in the literature so far, and is expected to trigger future experiments on the π*1σ photochemistry of molecules of chemical and biological importance. The design of the optimal pulses and their application to enhance the overall dissociation probability is carried out within the framework of optimal control theory. The quantum dynamics of the system in the presence of pulse is treated by solving the time-dependent Schrödinger equation in the semi-classical dipole approximation.

  10. Active Control of Separation From the Flap of a Supercritical Airfoil

    NASA Technical Reports Server (NTRS)

    Melton, LaTunia Pack; Yao, Chung-Sheng; Seifert, Avi

    2006-01-01

    Zero-mass-flux periodic excitation was applied at several regions on a simplified high-lift system to delay the occurrence of flow separation. The NASA Energy Efficient Transport (EET) supercritical airfoil was equipped with a 15% chord simply hinged leading edge flap and a 25% chord simply hinged trailing edge flap. Detailed flow features were measured in an attempt to identify optimal actuator placement. The measurements included steady and unsteady model and tunnel wall pressures, wake surveys, arrays of surface hot-films, flow visualization, and particle image velocimetry (PIV). The current paper describes the application of active separation control at several locations on the deflected trailing edge flap. High frequency (F(+) approximately equal to 10) and low frequency amplitude modulation (F(+) sub AM approximately equal to 1) of the high frequency excitation were used for control. It was noted that the same performance gains were obtained with amplitude modulation and required only 30% of the momentum input required by pure sine excitation.

  11. Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

    NASA Technical Reports Server (NTRS)

    Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

    2016-01-01

    A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

  12. Theory and Applications of Weakly Interacting Markov Processes

    DTIC Science & Technology

    2018-02-03

    Moderate deviation principles for stochastic dynamical systems. Boston University, Math Colloquium, March 27, 2015. • Moderate Deviation Principles for...Markov chain approximation method. Submitted. [8] E. Bayraktar and M. Ludkovski. Optimal trade execution in illiquid markets. Math . Finance, 21(4):681...701, 2011. [9] E. Bayraktar and M. Ludkovski. Liquidation in limit order books with controlled intensity. Math . Finance, 24(4):627–650, 2014. [10] P.D

  13. Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

    NASA Astrophysics Data System (ADS)

    Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

    2018-03-01

    The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

  14. The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

    2000-05-08

    The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin-orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin-orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation,more » the generalized gradient approximation and Hartree-Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin-orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work. (c) 2000 American Institute of Physics.« less

  15. Optimal control of energy extraction in LES of large wind farms

    NASA Astrophysics Data System (ADS)

    Meyers, Johan; Goit, Jay; Munters, Wim

    2014-11-01

    We investigate the use of optimal control combined with Large-Eddy Simulations (LES) of wind-farm boundary layer interaction for the increase of total energy extraction in very large ``infinite'' wind farms and in finite farms. We consider the individual wind turbines as flow actuators, whose energy extraction can be dynamically regulated in time so as to optimally influence the turbulent flow field, maximizing the wind farm power. For the simulation of wind-farm boundary layers we use large-eddy simulations in combination with an actuator-disk representation of wind turbines. Simulations are performed in our in-house pseudo-spectral code SP-Wind. For the optimal control study, we consider the dynamic control of turbine-thrust coefficients in the actuator-disk model. They represent the effect of turbine blades that can actively pitch in time, changing the lift- and drag coefficients of the turbine blades. In a first infinite wind-farm case, we find that farm power is increases by approximately 16% over one hour of operation. This comes at the cost of a deceleration of the outer layer of the boundary layer. A detailed analysis of energy balances is presented, and a comparison is made between infinite and finite farm cases, for which boundary layer entrainment plays an import role. The authors acknowledge support from the European Research Council (FP7-Ideas, Grant No. 306471). Simulations were performed on the computing infrastructure of the VSC Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Govern.

  16. A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

    NASA Astrophysics Data System (ADS)

    Voloshinov, V. V.

    2018-03-01

    In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

  17. Development of an hp-version finite element method for computational optimal control

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Warner, Michael S.

    1993-01-01

    The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.

  18. A well-posed optimal spectral element approximation for the Stokes problem

    NASA Technical Reports Server (NTRS)

    Maday, Y.; Patera, A. T.; Ronquist, E. M.

    1987-01-01

    A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

  19. On the role of the optimization algorithm of RapidArc(®) volumetric modulated arc therapy on plan quality and efficiency.

    PubMed

    Vanetti, Eugenio; Nicolini, Giorgia; Nord, Janne; Peltola, Jarkko; Clivio, Alessandro; Fogliata, Antonella; Cozzi, Luca

    2011-11-01

    The RapidArc volumetric modulated arc therapy (VMAT) planning process is based on a core engine, the so-called progressive resolution optimizer (PRO). This is the optimization algorithm used to determine the combination of field shapes, segment weights (with dose rate and gantry speed variations), which best approximate the desired dose distribution in the inverse planning problem. A study was performed to assess the behavior of two versions of PRO. These two versions mostly differ in the way continuous variables describing the modulated arc are sampled into discrete control points, in the planning efficiency and in the presence of some new features. The analysis aimed to assess (i) plan quality, (ii) technical delivery aspects, (iii) agreement between delivery and calculations, and (iv) planning efficiency of the two versions. RapidArc plans were generated for four groups of patients (five patients each): anal canal, advanced lung, head and neck, and multiple brain metastases and were designed to test different levels of planning complexity and anatomical features. Plans from optimization with PRO2 (first generation of RapidArc optimizer) were compared against PRO3 (second generation of the algorithm). Additional plans were optimized with PRO3 using new features: the jaw tracking, the intermediate dose and the air cavity correction options. Results showed that (i) plan quality was generally improved with PRO3 and, although not for all parameters, some of the scored indices showed a macroscopic improvement with PRO3. (ii) PRO3 optimization leads to simpler patterns of the dynamic parameters particularly for dose rate. (iii) No differences were observed between the two algorithms in terms of pretreatment quality assurance measurements and (iv) PRO3 optimization was generally faster, with a time reduction of a factor approximately 3.5 with respect to PRO2. These results indicate that PRO3 is either clinically beneficial or neutral in terms of dosimetric quality while it showed significant advantages in speed and technical aspects.

  20. Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

    NASA Astrophysics Data System (ADS)

    Beda, Tibi

    2006-10-01

    The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

  1. Real-World Application of Robust Design Optimization Assisted by Response Surface Approximation and Visual Data-Mining

    NASA Astrophysics Data System (ADS)

    Shimoyama, Koji; Jeong, Shinkyu; Obayashi, Shigeru

    A new approach for multi-objective robust design optimization was proposed and applied to a real-world design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relations between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.

  2. Structural physical approximation for the realization of the optimal singlet fraction with two measurements

    NASA Astrophysics Data System (ADS)

    Adhikari, Satyabrata

    2018-04-01

    Structural physical approximation (SPA) has been exploited to approximate nonphysical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of SPA to partial transpose is less than 2/9 then the two-qubit state is entangled. We find application of SPA to partial transpose in the estimation of the optimal singlet fraction. We show that the optimal singlet fraction can be expressed in terms of the minimum eigenvalue of SPA to partial transpose. We also show that the optimal singlet fraction can be realized using Hong-Ou-Mandel interferometry with only two detectors. Further we have shown that the generated hybrid entangled state between a qubit and a binary coherent state can be used as a resource state in quantum teleportation.

  3. Neural network robust tracking control with adaptive critic framework for uncertain nonlinear systems.

    PubMed

    Wang, Ding; Liu, Derong; Zhang, Yun; Li, Hongyi

    2018-01-01

    In this paper, we aim to tackle the neural robust tracking control problem for a class of nonlinear systems using the adaptive critic technique. The main contribution is that a neural-network-based robust tracking control scheme is established for nonlinear systems involving matched uncertainties. The augmented system considering the tracking error and the reference trajectory is formulated and then addressed under adaptive critic optimal control formulation, where the initial stabilizing controller is not needed. The approximate control law is derived via solving the Hamilton-Jacobi-Bellman equation related to the nominal augmented system, followed by closed-loop stability analysis. The robust tracking control performance is guaranteed theoretically via Lyapunov approach and also verified through simulation illustration. Copyright © 2017 Elsevier Ltd. All rights reserved.

  4. Capture and separation of l-histidine through optimized zinc-decorated magnetic silica spheres.

    PubMed

    Cardoso, Vanessa F; Sebastián, Víctor; Silva, Carlos J R; Botelho, Gabriela; Lanceros-Méndez, Senentxu

    2017-09-01

    Zinc-decorated magnetic silica spheres were developed, optimized and tested for the capture and separation of l-histidine. The magnetic silica spheres were prepared using a simple sol-gel method and show excellent magnetic characteristics, adsorption capacity toward metal ions, and stability in aqueous solution in a wide pH range. The binding capacity of zinc-decorated magnetic silica spheres to histidine proved to be strongly influenced by the morphology, composition and concentration of metal at the surface of the magnetic silica spheres and therefore these parameters should be carefully controlled in order to maximize the performance for protein purification purposes. Optimized zinc-decorated magnetic silica spheres demonstrate a binding capacity to l-histidine of approximately 44mgg -1 at the optimum binding pH buffer. Copyright © 2017 Elsevier B.V. All rights reserved.

  5. Speckle-metric-optimization-based adaptive optics for laser beam projection and coherent beam combining.

    PubMed

    Vorontsov, Mikhail; Weyrauch, Thomas; Lachinova, Svetlana; Gatz, Micah; Carhart, Gary

    2012-07-15

    Maximization of a projected laser beam's power density at a remotely located extended object (speckle target) can be achieved by using an adaptive optics (AO) technique based on sensing and optimization of the target-return speckle field's statistical characteristics, referred to here as speckle metrics (SM). SM AO was demonstrated in a target-in-the-loop coherent beam combining experiment using a bistatic laser beam projection system composed of a coherent fiber-array transmitter and a power-in-the-bucket receiver. SM sensing utilized a 50 MHz rate dithering of the projected beam that provided a stair-mode approximation of the outgoing combined beam's wavefront tip and tilt with subaperture piston phases. Fiber-integrated phase shifters were used for both the dithering and SM optimization with stochastic parallel gradient descent control.

  6. Exact and Approximate Stability of Solutions to Traveling Salesman Problems.

    PubMed

    Niendorf, Moritz; Girard, Anouck R

    2018-02-01

    This paper presents the stability analysis of an optimal tour for the symmetric traveling salesman problem (TSP) by obtaining stability regions. The stability region of an optimal tour is the set of all cost changes for which that solution remains optimal and can be understood as the margin of optimality for a solution with respect to perturbations in the problem data. It is known that it is not possible to test in polynomial time whether an optimal tour remains optimal after the cost of an arbitrary set of edges changes. Therefore, this paper develops tractable methods to obtain under and over approximations of stability regions based on neighborhoods and relaxations. The application of the results to the two-neighborhood and the minimum 1 tree (M1T) relaxation are discussed in detail. For Euclidean TSPs, stability regions with respect to vertex location perturbations and the notion of safe radii and location criticalities are introduced. Benefits of this paper include insight into robustness properties of tours, minimum spanning trees, M1Ts, and fast methods to evaluate optimality after perturbations occur. Numerical examples are given to demonstrate the methods and achievable approximation quality.

  7. Optimal partitioning of random programs across two processors

    NASA Technical Reports Server (NTRS)

    Nicol, D. M.

    1986-01-01

    The optimal partitioning of random distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false.

  8. Cascade Optimization Strategy with Neural Network and Regression Approximations Demonstrated on a Preliminary Aircraft Engine Design

    NASA Technical Reports Server (NTRS)

    Hopkins, Dale A.; Patnaik, Surya N.

    2000-01-01

    A preliminary aircraft engine design methodology is being developed that utilizes a cascade optimization strategy together with neural network and regression approximation methods. The cascade strategy employs different optimization algorithms in a specified sequence. The neural network and regression methods are used to approximate solutions obtained from the NASA Engine Performance Program (NEPP), which implements engine thermodynamic cycle and performance analysis models. The new methodology is proving to be more robust and computationally efficient than the conventional optimization approach of using a single optimization algorithm with direct reanalysis. The methodology has been demonstrated on a preliminary design problem for a novel subsonic turbofan engine concept that incorporates a wave rotor as a cycle-topping device. Computations of maximum thrust were obtained for a specific design point in the engine mission profile. The results (depicted in the figure) show a significant improvement in the maximum thrust obtained using the new methodology in comparison to benchmark solutions obtained using NEPP in a manual design mode.

  9. Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

    NASA Technical Reports Server (NTRS)

    Martin, Rodney Alexander

    2009-01-01

    An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

  10. Design Process for High Speed Civil Transport Aircraft Improved by Neural Network and Regression Methods

    NASA Technical Reports Server (NTRS)

    Hopkins, Dale A.

    1998-01-01

    A key challenge in designing the new High Speed Civil Transport (HSCT) aircraft is determining a good match between the airframe and engine. Multidisciplinary design optimization can be used to solve the problem by adjusting parameters of both the engine and the airframe. Earlier, an example problem was presented of an HSCT aircraft with four mixed-flow turbofan engines and a baseline mission to carry 305 passengers 5000 nautical miles at a cruise speed of Mach 2.4. The problem was solved by coupling NASA Lewis Research Center's design optimization testbed (COMETBOARDS) with NASA Langley Research Center's Flight Optimization System (FLOPS). The computing time expended in solving the problem was substantial, and the instability of the FLOPS analyzer at certain design points caused difficulties. In an attempt to alleviate both of these limitations, we explored the use of two approximation concepts in the design optimization process. The two concepts, which are based on neural network and linear regression approximation, provide the reanalysis capability and design sensitivity analysis information required for the optimization process. The HSCT aircraft optimization problem was solved by using three alternate approaches; that is, the original FLOPS analyzer and two approximate (derived) analyzers. The approximate analyzers were calibrated and used in three different ranges of the design variables; narrow (interpolated), standard, and wide (extrapolated).

  11. A Luciferase Reporter Gene System for High-Throughput Screening of γ-Globin Gene Activators.

    PubMed

    Xie, Wensheng; Silvers, Robert; Ouellette, Michael; Wu, Zining; Lu, Quinn; Li, Hu; Gallagher, Kathleen; Johnson, Kathy; Montoute, Monica

    2016-01-01

    Luciferase reporter gene assays have long been used for drug discovery due to their high sensitivity and robust signal. A dual reporter gene system contains a gene of interest and a control gene to monitor non-specific effects on gene expression. In our dual luciferase reporter gene system, a synthetic promoter of γ-globin gene was constructed immediately upstream of the firefly luciferase gene, followed downstream by a synthetic β-globin gene promoter in front of the Renilla luciferase gene. A stable cell line with the dual reporter gene was cloned and used for all assay development and HTS work. Due to the low activity of the control Renilla luciferase, only the firefly luciferase activity was further optimized for HTS. Several critical factors, such as cell density, serum concentration, and miniaturization, were optimized using tool compounds to achieve maximum robustness and sensitivity. Using the optimized reporter assay, the HTS campaign was successfully completed and approximately 1000 hits were identified. In this chapter, we also describe strategies to triage hits that non-specifically interfere with firefly luciferase.

  12. Capture of near-Earth objects with low-thrust propulsion and invariant manifolds

    NASA Astrophysics Data System (ADS)

    Tang, Gao; Jiang, Fanghua

    2016-01-01

    In this paper, a mission incorporating low-thrust propulsion and invariant manifolds to capture near-Earth objects (NEOs) is investigated. The initial condition has the spacecraft rendezvousing with the NEO. The mission terminates once it is inserted into a libration point orbit (LPO). The spacecraft takes advantage of stable invariant manifolds for low-energy ballistic capture. Low-thrust propulsion is employed to retrieve the joint spacecraft-asteroid system. Global optimization methods are proposed for the preliminary design. Local direct and indirect methods are applied to optimize the two-impulse transfers. Indirect methods are implemented to optimize the low-thrust trajectory and estimate the largest retrievable mass. To overcome the difficulty that arises from bang-bang control, a homotopic approach is applied to find an approximate solution. By detecting the switching moments of the bang-bang control the efficiency and accuracy of numerical integration are guaranteed. By using the homotopic approach as the initial guess the shooting function is easy to solve. The relationship between the maximum thrust and the retrieval mass is investigated. We find that both numerically and theoretically a larger thrust is preferred.

  13. Progress in the Phase 0 Model Development of a STAR Concept for Dynamics and Control Testing

    NASA Technical Reports Server (NTRS)

    Woods-Vedeler, Jessica A.; Armand, Sasan C.

    2003-01-01

    The paper describes progress in the development of a lightweight, deployable passive Synthetic Thinned Aperture Radiometer (STAR). The spacecraft concept presented will enable the realization of 10 km resolution global soil moisture and ocean salinity measurements at 1.41 GHz. The focus of this work was on definition of an approximately 1/3-scaled, 5-meter Phase 0 test article for concept demonstration and dynamics and control testing. Design requirements, parameters and a multi-parameter, hybrid scaling approach for the dynamically scaled test model were established. The El Scaling Approach that was established allows designers freedom to define the cross section of scaled, lightweight structural components that is most convenient for manufacturing when the mass of the component is small compared to the overall system mass. Static and dynamic response analysis was conducted on analytical models to evaluate system level performance and to optimize panel geometry for optimal tension load distribution.

  14. Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

    NASA Astrophysics Data System (ADS)

    Zhang, Huan; Dower, Peter M.

    2012-09-01

    Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

  15. Regularization by Functions of Bounded Variation and Applications to Image Enhancement

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Casas, E.; Kunisch, K.; Pola, C.

    1999-09-15

    Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise.

  16. Structural tailoring of counter rotation propfans

    NASA Technical Reports Server (NTRS)

    Brown, Kenneth W.; Hopkins, D. A.

    1989-01-01

    The STAT program was designed for the optimization of single rotation, tractor propfan designs. New propfan designs, however, generally consist of two counter rotating propfan rotors. STAT is constructed to contain two levels of analysis. An interior loop, consisting of accurate, efficient approximate analyses, is used to perform the primary propfan optimization. Once an optimum design has been obtained, a series of refined analyses are conducted. These analyses, while too computer time expensive for the optimization loop, are of sufficient accuracy to validate the optimized design. Should the design prove to be unacceptable, provisions are made for recalibration of the approximate analyses, for subsequent reoptimization.

  17. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zamzam, Ahmed, S.; Zhaoy, Changhong; Dall'Anesey, Emiliano

    This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated usingmore » two unbalanced multiphase distribution feeders with both wye and delta connections.« less

  18. Approximation of the Newton Step by a Defect Correction Process

    NASA Technical Reports Server (NTRS)

    Arian, E.; Batterman, A.; Sachs, E. W.

    1999-01-01

    In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in Generalized Minimum Residual (GMRES). We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES.

  19. Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

    USGS Publications Warehouse

    Naff, R.L.; Russell, T.F.; Wilson, J.D.; ,; ,; ,; ,; ,

    2000-01-01

    Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

  20. Optimal Chebyshev polynomials on ellipses in the complex plane

    NASA Technical Reports Server (NTRS)

    Fischer, Bernd; Freund, Roland

    1989-01-01

    The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

  1. Stabilization of business cycles of finance agents using nonlinear optimal control

    NASA Astrophysics Data System (ADS)

    Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

    2017-11-01

    Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

  2. Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liang, Faming; Cheng, Yichen; Lin, Guang

    2014-06-13

    Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« less

  3. Annual Review of Research under the Joint Services Electronics Program,

    DTIC Science & Technology

    1981-12-01

    nonlinear system under investigation to be transformed, without approximation, into an equivalent linear system to which classical design methodologies are...employed his work in the design of an experimental helicopter autopilot which is presently under- going simulation and is expected to fly in the near...decentralized, and non -quad- duced from that which would be required ratic systems is presented. Here, one for an optimal non -linlar controller. designs a

  4. Resonant cryogenic chopper. [for infrared and submillimeter radiometers

    NASA Technical Reports Server (NTRS)

    Page, Lyman A.; Cheng, Edward S.; Meyer, Stephan S.

    1992-01-01

    An account is given of the design features, construction, and performance of a both mechanically and thermally robust, resonant cryogenic chopper operating at 4.2 K. The chopper can occult a 2.54-cm aperture at 4.5 Hz, with approximately 1-mW dissipation. The controllability of the stator and rotor magnetic fields facilitates performance optimization and the determination of any possible interference effects. Attention is given to long-term amplitude stability determinations.

  5. Polymeric Materials Models in the Warrior Injury Assessment Manikin (WIAMan) Anthropomorphic Test Device (ATD) Tech Demonstrator

    DTIC Science & Technology

    2017-01-01

    are the shear relaxation moduli and relaxation times , which make up the classical Prony series . A Prony- series expansion is a relaxation function...approximation for modeling time -dependent damping. The scalar parameters 1 and 2 control the nonlinearity of the Prony series . Under the...Velodyne that best fit the experimental stress-strain data. To do so, the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA

  6. An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wilson, B.G.

    1999-11-11

    The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

  7. Promoter library-based module combination (PLMC) technology for optimization of threonine biosynthesis in Corynebacterium glutamicum.

    PubMed

    Wei, Liang; Xu, Ning; Wang, Yiran; Zhou, Wei; Han, Guoqiang; Ma, Yanhe; Liu, Jun

    2018-05-01

    Due to the lack of efficient control elements and tools, the fine-tuning of gene expression in the multi-gene metabolic pathways is still a great challenge for engineering microbial cell factories, especially for the important industrial microorganism Corynebacterium glutamicum. In this study, the promoter library-based module combination (PLMC) technology was developed to efficiently optimize the expression of genes in C. glutamicum. A random promoter library was designed to contain the putative - 10 (NNTANANT) and - 35 (NNGNCN) consensus motifs, and refined through a three-step screening procedure to achieve numerous genetic control elements with different strength levels, including fluorescence-activated cell sorting (FACS) screening, agar plate screening, and 96-well plate screening. Multiple conventional strategies were employed for further precise characterizations of the promoter library, such as real-time quantitative PCR, sodium dodecyl sulfate polyacrylamide gel electrophoresis, FACS analysis, and the lacZ reporter system. These results suggested that the established promoter elements effectively regulated gene expression and showed varying strengths over a wide range. Subsequently, a multi-module combination technology was created based on the efficient promoter elements for combination and optimization of modules in the multi-gene pathways. Using this technology, the threonine biosynthesis pathway was reconstructed and optimized by predictable tuning expression of five modules in C. glutamicum. The threonine titer of the optimized strain was significantly improved to 12.8 g/L, an approximate 6.1-fold higher than that of the control strain. Overall, the PLMC technology presented in this study provides a rapid and effective method for combination and optimization of multi-gene pathways in C. glutamicum.

  8. Energy extraction from atmospheric turbulence to improve flight vehicle performance

    NASA Astrophysics Data System (ADS)

    Patel, Chinmay Karsandas

    Small 'bird-sized' Unmanned Aerial Vehicles (UAVs) have now become practical due to technological advances in embedded electronics, miniature sensors and actuators, and propulsion systems. Birds are known to take advantage of wind currents to conserve energy and fly long distances without flapping their wings. This dissertation explores the possibility of improving the performance of small UAVs by extracting the energy available in atmospheric turbulence. An aircraft can gain energy from vertical gusts by increasing its lift in regions of updraft and reducing its lift in downdrafts - a concept that has been known for decades. Starting with a simple model of a glider flying through a sinusoidal gust, a parametric optimization approach is used to compute the minimum gust amplitude and optimal control input required for the glider to sustain flight without losing energy. For small UAVs using optimal control inputs, sinusoidal gusts with amplitude of 10--15% of the cruise speed are sufficient to keep the aircraft aloft. The method is then modified and extended to include random gusts that are representative of natural turbulence. A procedure to design optimal control laws for energy extraction from realistic gust profiles is developed using a Genetic Algorithm (GA). A feedback control law is designed to perform well over a variety of random gusts, and not be tailored for one particular gust. A small UAV flying in vertical turbulence is shown to obtain average energy savings of 35--40% with the use of a simple control law. The design procedure is also extended to determine optimal control laws for sinusoidal as well as turbulent lateral gusts. The theoretical work is complemented by experimental validation using a small autonomous UAV. The development of a lightweight autopilot and UAV platform is presented. Flight test results show that active control of the lift of an autonomous glider resulted in approximately 46% average energy savings compared to glides with fixed control surfaces. Statistical analysis of test samples shows that 19% of the active control test runs resulted in no energy loss, thus demonstrating the potential of the 'gust soaring' concept to dramatically improve the performance of small UAVs.

  9. Distributed System Optimal Control and Parameter Estimation: Computational Techniques Using Spline Approximations.

    DTIC Science & Technology

    1982-04-01

    orthogonal proJec- differential equations (PDE) of hyperbolic or tion of Z onto ZN and N -pN’/PN. This parabolic type. Roughly speaking, in each results in...to choose a parameter from an sipative inequality in Z (such asə(q)ZZ> admissible set Q so as to yield a best fit < W < z,z> for z E Dom (.&(q))and .W...semigroup T(t;q). The approxi- sumed fixed and known and F in (1) is a N control input term , say F(t) = Bu(t). Then mating operators. S1(q) are defined

  10. Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.

    PubMed

    Yang, Qinmin; Jagannathan, Sarangapani

    2012-04-01

    In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.

  11. Online optimal obstacle avoidance for rotary-wing autonomous unmanned aerial vehicles

    NASA Astrophysics Data System (ADS)

    Kang, Keeryun

    This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. The flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.

  12. Large deviations and portfolio optimization

    NASA Astrophysics Data System (ADS)

    Sornette, Didier

    Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation. A major item is that risk, usually thought of as one-dimensional in the conventional mean-variance approach, has to be addressed by the full distribution of losses. Furthermore, the time-horizon of the investment is shown to play a major role. We show the importance of accounting for large fluctuations and use the theory of Cramér for large deviations in this context. We first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes, and the different optimal strategies for the investors depending on their size. We then analyze the case of assets whose price variations are distributed according to exponential laws, a situation that is found to describe daily price variations reasonably well. Several portfolio optimization strategies are presented that aim at controlling large risks. We end by extending the standard mean-variance portfolio optimization theory, first within the quasi-Gaussian approximation and then using a general formulation for non-Gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena.

  13. Physical and hydraulic properties of baked ceramic aggregates used for plant growth medium

    NASA Technical Reports Server (NTRS)

    Steinberg, Susan L.; Kluitenberg, Gerard J.; Jones, Scott B.; Daidzic, Nihad E.; Reddi, Lakshmi N.; Xiao, Ming; Tuller, Markus; Newman, Rebecca M.; Or, Dani; Alexander, J. Iwan. D.

    2005-01-01

    Baked ceramic aggregates (fritted clay, arcillite) have been used for plant research both on the ground and in microgravity. Optimal control of water and air within the root zone in any gravity environment depends on physical and hydraulic properties of the aggregate, which were evaluated for 0.25-1-mm and 1-2-mm particle size distributions. The maximum bulk densities obtained by any packing technique were 0.68 and 0.64 g cm-3 for 0.25-1-mm and 1-2-mm particles, respectively. Wettable porosity obtained by infiltration with water was approximately 65%, substantially lower than total porosity of approximately 74%. Aggregate of both particle sizes exhibited a bimodal pore size distribution consisting of inter-aggregate macropores and intra-aggregate micropores, with the transition from macro- to microporosity beginning at volumetric water content of approximately 36% to 39%. For inter-aggregate water contents that support optimal plant growth there is 45% change in water content that occurs over a relatively small matric suction range of 0-20 cm H2O for 0.25-1-mm and 0 to -10 cm H2O for 1-2-mm aggregate. Hysteresis is substantial between draining and wetting aggregate, which results in as much as a approximately 10% to 20% difference in volumetric water content for a given matric potential. Hydraulic conductivity was approximately an order of magnitude higher for 1-2-mm than for 0.25-1-mm aggregate until significant drainage of the inter-aggregate pore space occurred. The large change in water content for a relatively small change in matric potential suggests that significant differences in water retention may be observed in microgravity as compared to earth.

  14. Optimal aeroassisted coplanar orbital transfer using an energy model

    NASA Technical Reports Server (NTRS)

    Halyo, Nesim; Taylor, Deborah B.

    1989-01-01

    The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

  15. Effective learning strategies for real-time image-guided adaptive control of multiple-source hyperthermia applicators.

    PubMed

    Cheng, Kung-Shan; Dewhirst, Mark W; Stauffer, Paul R; Das, Shiva

    2010-03-01

    This paper investigates overall theoretical requirements for reducing the times required for the iterative learning of a real-time image-guided adaptive control routine for multiple-source heat applicators, as used in hyperthermia and thermal ablative therapy for cancer. Methods for partial reconstruction of the physical system with and without model reduction to find solutions within a clinically practical timeframe were analyzed. A mathematical analysis based on the Fredholm alternative theorem (FAT) was used to compactly analyze the existence and uniqueness of the optimal heating vector under two fundamental situations: (1) noiseless partial reconstruction and (2) noisy partial reconstruction. These results were coupled with a method for further acceleration of the solution using virtual source (VS) model reduction. The matrix approximation theorem (MAT) was used to choose the optimal vectors spanning the reduced-order subspace to reduce the time for system reconstruction and to determine the associated approximation error. Numerical simulations of the adaptive control of hyperthermia using VS were also performed to test the predictions derived from the theoretical analysis. A thigh sarcoma patient model surrounded by a ten-antenna phased-array applicator was retained for this purpose. The impacts of the convective cooling from blood flow and the presence of sudden increase of perfusion in muscle and tumor were also simulated. By FAT, partial system reconstruction directly conducted in the full space of the physical variables such as phases and magnitudes of the heat sources cannot guarantee reconstructing the optimal system to determine the global optimal setting of the heat sources. A remedy for this limitation is to conduct the partial reconstruction within a reduced-order subspace spanned by the first few maximum eigenvectors of the true system matrix. By MAT, this VS subspace is the optimal one when the goal is to maximize the average tumor temperature. When more than 6 sources present, the steps required for a nonlinear learning scheme is theoretically fewer than that of a linear one, however, finite number of iterative corrections is necessary for a single learning step of a nonlinear algorithm. Thus, the actual computational workload for a nonlinear algorithm is not necessarily less than that required by a linear algorithm. Based on the analysis presented herein, obtaining a unique global optimal heating vector for a multiple-source applicator within the constraints of real-time clinical hyperthermia treatments and thermal ablative therapies appears attainable using partial reconstruction with minimum norm least-squares method with supplemental equations. One way to supplement equations is the inclusion of a method of model reduction.

  16. Formation Flight System Extremum-Seeking-Control Using Blended Performance Parameters

    NASA Technical Reports Server (NTRS)

    Ryan, John J. (Inventor)

    2018-01-01

    An extremum-seeking control system for formation flight that uses blended performance parameters in a conglomerate performance function that better approximates drag reduction than performance functions formed from individual measurements. Generally, a variety of different measurements are taken and fed to a control system, the measurements are weighted, and are then subjected to a peak-seeking control algorithm. As measurements are continually taken, the aircraft will be guided to a relative position which optimizes the drag reduction of the formation. Two embodiments are discussed. Two approaches are shown for determining relative weightings: "a priori" by which they are qualitatively determined (by minimizing the error between the conglomerate function and the drag reduction function), and by periodically updating the weightings as the formation evolves.

  17. Experimental confirmation of a PDE-based approach to design of feedback controls

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Smith, Ralph C.; Brown, D. E.; Silcox, R. J.; Metcalf, Vern L.

    1995-01-01

    Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

  18. Aerodynamic control, recovery, and sensor design for a first stage flyback booster

    NASA Technical Reports Server (NTRS)

    1989-01-01

    The mission of the flyback group is to control and recover the first stage of a commercially developed winged booster launched from a B-52 at 40,000 ft and Mach 0.8. First-stage separation occurs at 210,000 ft and Mach 8.7; the second and third stages will continue deployment of their 600 lb payload into low Earth orbit. The job of the flyback group begins at this point, employing a modified control system developed to stabilize and maneuver the separated first-stage vehicle to a suitable landing site approximately 130 miles from the launch point over the Pacific Ocean. This multidisciplinary design was accomplished by four subgroups: aerodynamic design/vehicle configuration (ADVC), trajectory optimization, controls, and thermal management.

  19. Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

    NASA Astrophysics Data System (ADS)

    Vinding, Mads S.; Maximov, Ivan I.; Tošner, Zdeněk; Nielsen, Niels Chr.

    2012-08-01

    The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B0) and rf field (B1) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.

  20. Fully Mechanically Controlled Automated Electron Microscopic Tomography

    DOE PAGES

    Liu, Jinxin; Li, Hongchang; Zhang, Lei; ...

    2016-07-11

    Knowledge of three-dimensional (3D) structures of each individual particles of asymmetric and flexible proteins is essential in understanding those proteins' functions; but their structures are difficult to determine. Electron tomography (ET) provides a tool for imaging a single and unique biological object from a series of tilted angles, but it is challenging to image a single protein for three-dimensional (3D) reconstruction due to the imperfect mechanical control capability of the specimen goniometer under both a medium to high magnification (approximately 50,000-160,000×) and an optimized beam coherence condition. Here, we report a fully mechanical control method for automating ET data acquisitionmore » without using beam tilt/shift processes. This method could reduce the accumulation of beam tilt/shift that used to compensate the error from the mechanical control, but downgraded the beam coherence. Our method was developed by minimizing the error of the target object center during the tilting process through a closed-loop proportional-integral (PI) control algorithm. The validations by both negative staining (NS) and cryo-electron microscopy (cryo-EM) suggest that this method has a comparable capability to other ET methods in tracking target proteins while maintaining optimized beam coherence conditions for imaging.« less

  1. Model Predictive Control considering Reachable Range of Wheels for Leg / Wheel Mobile Robots

    NASA Astrophysics Data System (ADS)

    Suzuki, Naito; Nonaka, Kenichiro; Sekiguchi, Kazuma

    2016-09-01

    Obstacle avoidance is one of the important tasks for mobile robots. In this paper, we study obstacle avoidance control for mobile robots equipped with four legs comprised of three DoF SCARA leg/wheel mechanism, which enables the robot to change its shape adapting to environments. Our previous method achieves obstacle avoidance by model predictive control (MPC) considering obstacle size and lateral wheel positions. However, this method does not ensure existence of joint angles which achieves reference wheel positions calculated by MPC. In this study, we propose a model predictive control considering reachable mobile ranges of wheels positions by combining multiple linear constraints, where each reachable mobile range is approximated as a convex trapezoid. Thus, we achieve to formulate a MPC as a quadratic problem with linear constraints for nonlinear problem of longitudinal and lateral wheel position control. By optimization of MPC, the reference wheel positions are calculated, while each joint angle is determined by inverse kinematics. Considering reachable mobile ranges explicitly, the optimal joint angles are calculated, which enables wheels to reach the reference wheel positions. We verify its advantages by comparing the proposed method with the previous method through numerical simulations.

  2. Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

    PubMed

    Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

    2017-03-01

    H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

  3. Quantifying the economic benefits of prevention in a healthcare setting with severe financial constraints: the case of hypertension control.

    PubMed

    Athanasakis, Kostas; Kyriopoulos, Ilias-Ioannis; Boubouchairopoulou, Nadia; Stergiou, George S; Kyriopoulos, John

    2015-01-01

    Hypertension significantly contributes to the increased cardiovascular morbidity and mortality, thus leading to rising healthcare costs. The objective of this study was to quantify the clinical and economic benefits of optimal systolic blood pressure (SBP), in a setting under severe financial constraints, as in the case of Greece. Hence, a Markov model projecting 10-year outcomes and costs was adopted, in order to compare two scenarios. The first one depicted the "current setting", where all hypertensives in Greece presented an average SBP of 164 mmHg, while the second scenario namely "optimal SBP control" represented a hypothesis in which the whole population of hypertensives would achieve optimal SBP (i.e. <140 mmHg). Cardiovascular events' occurrence was estimated for four sub-models (according to gender and smoking status). Costs were calculated from the Greek healthcare system's perspective (discounted at a 3% annual rate). Findings showed that compared to the "current setting", universal "optimal SBP control" could, within a 10-year period, reduce the occurrence of non-fatal events and deaths, by 80 and 61 cases/1000 male smokers; 59 and 37 cases/1000 men non-smokers; whereas the respective figures for women were 69 and 57 cases/1000 women smokers; and accordingly, 52 and 28 cases/1000 women non-smokers. Considering health expenditures, they could be reduced by approximately €83 million per year. Therefore, prevention of cardiovascular events through BP control could result in reduced morbidity, thereby in substantial cost savings. Based on clinical and economic outcomes, interventions that promote BP control should be a health policy priority.

  4. Minimizing stellarator turbulent transport by geometric optimization

    NASA Astrophysics Data System (ADS)

    Mynick, H. E.

    2010-11-01

    Up to now, a transport optimized stellarator has meant one optimized to minimize neoclassical transport,ootnotetextH.E. Mynick, Phys. Plasmas 13, 058102 (2006). while the task of also mitigating turbulent transport, usually the dominant transport channel in such designs, has not been addressed, due to the complexity of plasma turbulence in stellarators. However, with the advent of gyrokinetic codes valid for 3D geometries such as GENE,ootnotetextF. Jenko, W. Dorland, M. Kotschenreuther, B.N. Rogers, Phys. Plasmas 7, 1904 (2000). and stellarator optimization codes such as STELLOPT,ootnotetextA. Reiman, G. Fu, S. Hirshman, L. Ku, et al, Plasma Phys. Control. Fusion 41 B273 (1999). designing stellarators to also reduce turbulent transport has become a realistic possibility. We have been using GENE to characterize the dependence of turbulent transport on stellarator geometry,ootnotetextH.E Mynick, P.A. Xanthopoulos, A.H. Boozer, Phys.Plasmas 16 110702 (2009). and to identify key geometric quantities which control the transport level. From the information obtained from these GENE studies, we are developing proxy functions which approximate the level of turbulent transport one may expect in a machine of a given geometry, and have extended STELLOPT to use these in its cost function, obtaining stellarator configurations with turbulent transport levels substantially lower than those in the original designs.

  5. Rational decision-making in inhibitory control.

    PubMed

    Shenoy, Pradeep; Yu, Angela J

    2011-01-01

    An important aspect of cognitive flexibility is inhibitory control, the ability to dynamically modify or cancel planned actions in response to changes in the sensory environment or task demands. We formulate a probabilistic, rational decision-making framework for inhibitory control in the stop signal paradigm. Our model posits that subjects maintain a Bayes-optimal, continually updated representation of sensory inputs, and repeatedly assess the relative value of stopping and going on a fine temporal scale, in order to make an optimal decision on when and whether to go on each trial. We further posit that they implement this continual evaluation with respect to a global objective function capturing the various reward and penalties associated with different behavioral outcomes, such as speed and accuracy, or the relative costs of stop errors and go errors. We demonstrate that our rational decision-making model naturally gives rise to basic behavioral characteristics consistently observed for this paradigm, as well as more subtle effects due to contextual factors such as reward contingencies or motivational factors. Furthermore, we show that the classical race model can be seen as a computationally simpler, perhaps neurally plausible, approximation to optimal decision-making. This conceptual link allows us to predict how the parameters of the race model, such as the stopping latency, should change with task parameters and individual experiences/ability.

  6. Rational Decision-Making in Inhibitory Control

    PubMed Central

    Shenoy, Pradeep; Yu, Angela J.

    2011-01-01

    An important aspect of cognitive flexibility is inhibitory control, the ability to dynamically modify or cancel planned actions in response to changes in the sensory environment or task demands. We formulate a probabilistic, rational decision-making framework for inhibitory control in the stop signal paradigm. Our model posits that subjects maintain a Bayes-optimal, continually updated representation of sensory inputs, and repeatedly assess the relative value of stopping and going on a fine temporal scale, in order to make an optimal decision on when and whether to go on each trial. We further posit that they implement this continual evaluation with respect to a global objective function capturing the various reward and penalties associated with different behavioral outcomes, such as speed and accuracy, or the relative costs of stop errors and go errors. We demonstrate that our rational decision-making model naturally gives rise to basic behavioral characteristics consistently observed for this paradigm, as well as more subtle effects due to contextual factors such as reward contingencies or motivational factors. Furthermore, we show that the classical race model can be seen as a computationally simpler, perhaps neurally plausible, approximation to optimal decision-making. This conceptual link allows us to predict how the parameters of the race model, such as the stopping latency, should change with task parameters and individual experiences/ability. PMID:21647306

  7. LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

    PubMed

    Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

    2017-03-01

    In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

  8. Experimental verification of a real-time tuning method of a model-based controller by perturbations to its poles

    NASA Astrophysics Data System (ADS)

    Kajiwara, Itsuro; Furuya, Keiichiro; Ishizuka, Shinichi

    2018-07-01

    Model-based controllers with adaptive design variables are often used to control an object with time-dependent characteristics. However, the controller's performance is influenced by many factors such as modeling accuracy and fluctuations in the object's characteristics. One method to overcome these negative factors is to tune model-based controllers. Herein we propose an online tuning method to maintain control performance for an object that exhibits time-dependent variations. The proposed method employs the poles of the controller as design variables because the poles significantly impact performance. Specifically, we use the simultaneous perturbation stochastic approximation (SPSA) to optimize a model-based controller with multiple design variables. Moreover, a vibration control experiment of an object with time-dependent characteristics as the temperature is varied demonstrates that the proposed method allows adaptive control and stably maintains the closed-loop characteristics.

  9. A Distribution-class Locational Marginal Price (DLMP) Index for Enhanced Distribution Systems

    NASA Astrophysics Data System (ADS)

    Akinbode, Oluwaseyi Wemimo

    The smart grid initiative is the impetus behind changes that are expected to culminate into an enhanced distribution system with the communication and control infrastructure to support advanced distribution system applications and resources such as distributed generation, energy storage systems, and price responsive loads. This research proposes a distribution-class analog of the transmission LMP (DLMP) as an enabler of the advanced applications of the enhanced distribution system. The DLMP is envisioned as a control signal that can incentivize distribution system resources to behave optimally in a manner that benefits economic efficiency and system reliability and that can optimally couple the transmission and the distribution systems. The DLMP is calculated from a two-stage optimization problem; a transmission system OPF and a distribution system OPF. An iterative framework that ensures accurate representation of the distribution system's price sensitive resources for the transmission system problem and vice versa is developed and its convergence problem is discussed. As part of the DLMP calculation framework, a DCOPF formulation that endogenously captures the effect of real power losses is discussed. The formulation uses piecewise linear functions to approximate losses. This thesis explores, with theoretical proofs, the breakdown of the loss approximation technique when non-positive DLMPs/LMPs occur and discusses a mixed integer linear programming formulation that corrects the breakdown. The DLMP is numerically illustrated in traditional and enhanced distribution systems and its superiority to contemporary pricing mechanisms is demonstrated using price responsive loads. Results show that the impact of the inaccuracy of contemporary pricing schemes becomes significant as flexible resources increase. At high elasticity, aggregate load consumption deviated from the optimal consumption by up to about 45 percent when using a flat or time-of-use rate. Individual load consumption deviated by up to 25 percent when using a real-time price. The superiority of the DLMP is more pronounced when important distribution network conditions are not reflected by contemporary prices. The individual load consumption incentivized by the real-time price deviated by up to 90 percent from the optimal consumption in a congested distribution network. While the DLMP internalizes congestion management, the consumption incentivized by the real-time price caused overloads.

  10. Application of IFT and SPSA to servo system control.

    PubMed

    Rădac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan

    2011-12-01

    This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.

  11. TECHNICAL DESIGN NOTE: Digital proportional-integral-derivative velocity controller of a Mössbauer spectrometer

    NASA Astrophysics Data System (ADS)

    Pechousek, J.; Prochazka, R.; Mashlan, M.; Jancik, D.; Frydrych, J.

    2009-01-01

    The digital proportional-integral-derivative (PID) velocity controller used in the Mössbauer spectrometer implemented in field programmable gate array (FPGA) is based on the National Instruments CompactRIO embedded system and LabVIEW graphical programming tools. The system works as a remote system accessible via the Ethernet. The digital controller operates in real-time conditions, and the maximum sampling frequency is approximately 227 kS s-1. The system was tested with standard sample measurements of α-Fe and α-57Fe2O3 on two different electromechanical velocity transducers. The nonlinearities of the velocity scales in the relative form are better than 0.2%. The replacement of the standard analog PID controller by the new system brings the possibility of optimizing the control process more precisely.

  12. Integrated System-Level Optimization for Concurrent Engineering With Parametric Subsystem Modeling

    NASA Technical Reports Server (NTRS)

    Schuman, Todd; DeWeck, Oliver L.; Sobieski, Jaroslaw

    2005-01-01

    The introduction of concurrent design practices to the aerospace industry has greatly increased the productivity of engineers and teams during design sessions as demonstrated by JPL's Team X. Simultaneously, advances in computing power have given rise to a host of potent numerical optimization methods capable of solving complex multidisciplinary optimization problems containing hundreds of variables, constraints, and governing equations. Unfortunately, such methods are tedious to set up and require significant amounts of time and processor power to execute, thus making them unsuitable for rapid concurrent engineering use. This paper proposes a framework for Integration of System-Level Optimization with Concurrent Engineering (ISLOCE). It uses parametric neural-network approximations of the subsystem models. These approximations are then linked to a system-level optimizer that is capable of reaching a solution quickly due to the reduced complexity of the approximations. The integration structure is described in detail and applied to the multiobjective design of a simplified Space Shuttle external fuel tank model. Further, a comparison is made between the new framework and traditional concurrent engineering (without system optimization) through an experimental trial with two groups of engineers. Each method is evaluated in terms of optimizer accuracy, time to solution, and ease of use. The results suggest that system-level optimization, running as a background process during integrated concurrent engineering sessions, is potentially advantageous as long as it is judiciously implemented.

  13. Improving multi-objective reservoir operation optimization with sensitivity-informed dimension reduction

    NASA Astrophysics Data System (ADS)

    Chu, J.; Zhang, C.; Fu, G.; Li, Y.; Zhou, H.

    2015-08-01

    This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed method dramatically reduces the computational demands required for attaining high-quality approximations of optimal trade-off relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed dimension reduction and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform dimension reduction of optimization problems when solving complex multi-objective reservoir operation problems.

  14. Multiagent Task Coordination Using a Distributed Optimization Approach

    DTIC Science & Technology

    2015-09-01

    positive- definite symmetric inertia matrix, C(q, q̇) ∈ <n×n is the centripetal and coriolis matrix, G(q) ∈ <n is the gravitation force vector, B(q) ∈ <n...artificial intelligence re- search are effectively integrated with the rigorous control systems analysis tools, and produced novel approximate dynamic...results are given to illustrate the effectiveness of the proposed designs. Section 7.0 concludes the report. 3.0 METHODS, ASSUMPTIONS, AND PROCEDURES

  15. Approximation in Optimal Control and Identification of Large Space Structures.

    DTIC Science & Technology

    1985-01-01

    I ease I Cr ’. ’. -4 . r*_...1- UN(D aSIFIED SECURITY CLAS.’ICATION OF fHIS P^.GE REPORT DOCUMENTATION PAGE 1 REPORT SECURITY CLASSIFICATION 1...RESTRICTIVE MARKINGS UNCLASSIFIED 2 SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORT Approved for public release; distribution 2b...NOS. PROGRAM PROJECT TASK WORK UNIT ELEMENT NO. NO. NO. NO Bolling AFB DC 20332-6448 61102F 2304 Al 11. TITLE IlnRCiude Security Claas.ifcation

  16. Deployable reflector antenna performance optimization using automated surface correction and array-feed compensation

    NASA Technical Reports Server (NTRS)

    Schroeder, Lyle C.; Bailey, M. C.; Mitchell, John L.

    1992-01-01

    Methods for increasing the electromagnetic (EM) performance of reflectors with rough surfaces were tested and evaluated. First, one quadrant of the 15-meter hoop-column antenna was retrofitted with computer-driven and controlled motors to allow automated adjustment of the reflector surface. The surface errors, measured with metric photogrammetry, were used in a previously verified computer code to calculate control motor adjustments. With this system, a rough antenna surface (rms of approximately 0.180 inch) was corrected in two iterations to approximately the structural surface smoothness limit of 0.060 inch rms. The antenna pattern and gain improved significantly as a result of these surface adjustments. The EM performance was evaluated with a computer program for distorted reflector antennas which had been previously verified with experimental data. Next, the effects of the surface distortions were compensated for in computer simulations by superimposing excitation from an array feed to maximize antenna performance relative to an undistorted reflector. Results showed that a 61-element array could produce EM performance improvements equal to surface adjustments. When both mechanical surface adjustment and feed compensation techniques were applied, the equivalent operating frequency increased from approximately 6 to 18 GHz.

  17. Belief Propagation Algorithm for Portfolio Optimization Problems

    PubMed Central

    2015-01-01

    The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

  18. Belief Propagation Algorithm for Portfolio Optimization Problems.

    PubMed

    Shinzato, Takashi; Yasuda, Muneki

    2015-01-01

    The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

  19. Cost-effectiveness of reducing sulfur emissions from ships.

    PubMed

    Wang, Chengfeng; Corbett, James J; Winebrake, James J

    2007-12-15

    We model cost-effectiveness of control strategies for reducing SO2 emissions from U.S. foreign commerce ships traveling in existing European or hypothetical U.S. West Coast SO(x) Emission Control Areas (SECAs) under international maritime regulations. Variation among marginal costs of control for individual ships choosing between fuel-switching and aftertreatment reveals cost-saving potential of economic incentive instruments. Compared to regulations prescribing low sulfur fuels, a performance-based policy can save up to $260 million for these ships with 80% more emission reductions than required because least-cost options on some individual ships outperform standards. Optimal simulation of a market-based SO2 control policy for approximately 4,700 U.S. foreign commerce ships traveling in the SECAs in 2002 shows that SECA emissions control targets can be achieved by scrubbing exhaust gas of one out of ten ships with annual savings up to $480 million over performance-based policy. A market-based policy could save the fleet approximately $63 million annually under our best-estimate scenario. Spatial evaluation of ship emissions reductions shows that market-based instruments can reduce more SO2 closer to land while being more cost-effective for the fleet. Results suggest that combining performance requirements with market-based instruments can most effectively control SO2 emissions from ships.

  20. Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

    NASA Technical Reports Server (NTRS)

    Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

    1998-01-01

    In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

  1. Local Approximation and Hierarchical Methods for Stochastic Optimization

    NASA Astrophysics Data System (ADS)

    Cheng, Bolong

    In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

  2. Evaluation of control laws and actuator locations for control systems applicable to deformable astronomical telescope mirrors

    NASA Technical Reports Server (NTRS)

    Ostroff, A. J.

    1973-01-01

    Some of the major difficulties associated with large orbiting astronomical telescopes are the cost of manufacturing the primary mirror to precise tolerances and the maintaining of diffraction-limited tolerances while in orbit. One successfully demonstrated approach for minimizing these problem areas is the technique of actively deforming the primary mirror by applying discrete forces to the rear of the mirror. A modal control technique, as applied to active optics, has previously been developed and analyzed. The modal control technique represents the plant to be controlled in terms of its eigenvalues and eigenfunctions which are estimated via numerical approximation techniques. The report includes an extension of previous work using the modal control technique and also describes an optimal feedback controller. The equations for both control laws are developed in state-space differential form and include such considerations as stability, controllability, and observability. These equations are general and allow the incorporation of various mode-analyzer designs; two design approaches are presented. The report also includes a technique for placing actuator and sensor locations at points on the mirror based upon the flexibility matrix of the uncontrolled or unobserved modes of the structure. The locations selected by this technique are used in the computer runs which are described. The results are based upon three different initial error distributions, two mode-analyzer designs, and both the modal and optimal control laws.

  3. Drag reduction of a car model by linear genetic programming control

    NASA Astrophysics Data System (ADS)

    Li, Ruiying; Noack, Bernd R.; Cordier, Laurent; Borée, Jacques; Harambat, Fabien

    2017-08-01

    We investigate open- and closed-loop active control for aerodynamic drag reduction of a car model. Turbulent flow around a blunt-edged Ahmed body is examined at ReH≈ 3× 105 based on body height. The actuation is performed with pulsed jets at all trailing edges (multiple inputs) combined with a Coanda deflection surface. The flow is monitored with 16 pressure sensors distributed at the rear side (multiple outputs). We apply a recently developed model-free control strategy building on genetic programming in Dracopoulos and Kent (Neural Comput Appl 6:214-228, 1997) and Gautier et al. (J Fluid Mech 770:424-441, 2015). The optimized control laws comprise periodic forcing, multi-frequency forcing and sensor-based feedback including also time-history information feedback and combinations thereof. Key enabler is linear genetic programming (LGP) as powerful regression technique for optimizing the multiple-input multiple-output control laws. The proposed LGP control can select the best open- or closed-loop control in an unsupervised manner. Approximately 33% base pressure recovery associated with 22% drag reduction is achieved in all considered classes of control laws. Intriguingly, the feedback actuation emulates periodic high-frequency forcing. In addition, the control identified automatically the only sensor which listens to high-frequency flow components with good signal to noise ratio. Our control strategy is, in principle, applicable to all multiple actuators and sensors experiments.

  4. Orbital dependent functionals: An atom projector augmented wave method implementation

    NASA Astrophysics Data System (ADS)

    Xu, Xiao

    This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

  5. Optimal approximations for risk measures of sums of lognormals based on conditional expectations

    NASA Astrophysics Data System (ADS)

    Vanduffel, S.; Chen, X.; Dhaene, J.; Goovaerts, M.; Henrard, L.; Kaas, R.

    2008-11-01

    In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S|[Lambda

  6. Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

    NASA Technical Reports Server (NTRS)

    Polsgrove, T.; Adams, R. B.; Brady, Hugh J. (Technical Monitor)

    2002-01-01

    Preliminary results are presented for two methods to approximate the mission performance of high specific impulse high specific power vehicles. The first method is based on an analytical approximation derived by Williams and Shepherd and can be used to approximate mission performance to outer planets and interstellar space. The second method is based on a parametric analysis of trajectories created using the well known trajectory optimization code, VARITOP. This parametric analysis allows the reader to approximate payload ratios and optimal power requirements for both one-way and round-trip missions. While this second method only addresses missions to and from Jupiter, future work will encompass all of the outer planet destinations and some interstellar precursor missions.

  7. Effectiveness and cost-effectiveness of erlotinib versus gefitinib in first-line treatment of epidermal growth factor receptor-activating mutation-positive non-small-cell lung cancer patients in Hong Kong.

    PubMed

    Lee, Vivian W Y; Schwander, Bjoern; Lee, Victor H F

    2014-06-01

    To compare the effectiveness and cost-effectiveness of erlotinib versus gefitinib as first-line treatment of epidermal growth factor receptor-activating mutation-positive non-small-cell lung cancer patients. DESIGN. Indirect treatment comparison and a cost-effectiveness assessment. Hong Kong. Those having epidermal growth factor receptor-activating mutation-positive non-small-cell lung cancer. Erlotinib versus gefitinib use was compared on the basis of four relevant Asian phase-III randomised controlled trials: one for erlotinib (OPTIMAL) and three for gefitinib (IPASS; NEJGSG; WJTOG). The cost-effectiveness assessment model simulates the transition between the health states: progression-free survival, progression, and death over a lifetime horizon. The World Health Organization criterion (incremental cost-effectiveness ratio <3 times of gross domestic product/capita:

  8. Grid integration and smart grid implementation of emerging technologies in electric power systems through approximate dynamic programming

    NASA Astrophysics Data System (ADS)

    Xiao, Jingjie

    A key hurdle for implementing real-time pricing of electricity is a lack of consumers' responses. Solutions to overcome the hurdle include the energy management system that automatically optimizes household appliance usage such as plug-in hybrid electric vehicle charging (and discharging with vehicle-to-grid) via a two-way communication with the grid. Real-time pricing, combined with household automation devices, has a potential to accommodate an increasing penetration of plug-in hybrid electric vehicles. In addition, the intelligent energy controller on the consumer-side can help increase the utilization rate of the intermittent renewable resource, as the demand can be managed to match the output profile of renewables, thus making the intermittent resource such as wind and solar more economically competitive in the long run. One of the main goals of this dissertation is to present how real-time retail pricing, aided by control automation devices, can be integrated into the wholesale electricity market under various uncertainties through approximate dynamic programming. What distinguishes this study from the existing work in the literature is that whole- sale electricity prices are endogenously determined as we solve a system operator's economic dispatch problem on an hourly basis over the entire optimization horizon. This modeling and algorithm framework will allow a feedback loop between electricity prices and electricity consumption to be fully captured. While we are interested in a near-optimal solution using approximate dynamic programming; deterministic linear programming benchmarks are use to demonstrate the quality of our solutions. The other goal of the dissertation is to use this framework to provide numerical evidence to the debate on whether real-time pricing is superior than the current flat rate structure in terms of both economic and environmental impacts. For this purpose, the modeling and algorithm framework is tested on a large-scale test case with hundreds of power plants based on data available for California, making our findings useful for policy makers, system operators and utility companies to gain a concrete understanding on the scale of the impact with real-time pricing.

  9. Long-term contraception in a small implant: A review of Suprelorin (deslorelin) studies in cats.

    PubMed

    Fontaine, Christelle

    2015-09-01

    Deslorelin (Suprelorin®; Virbac) is a gonadotropin-releasing hormone (GnRH) agonist licensed in select countries for the long-term suppression of fertility in adult male dogs and male ferrets. This article summarizes studies investigating the use of deslorelin implants for the long-term suppression of fertility in male and female domestic cats. Slow-release deslorelin implants have been shown to generate effective, safe and reversible long-term contraception in male and female cats. In pubertal cats, a 4.7 mg deslorelin implant suppressed steroid sex hormones for an average of approximately 20 months (range 15-25 months) in males and an average of approximately 24 months (range 16-37 months) in females. Reversibility has been demonstrated by fertile matings approximately 2 years post-treatment in both male and female adult cats. In prepubertal female cats of approximately 4 months of age, puberty was postponed to an average of approximately 10 months of age (range 6-15 months) by a 4.7 mg deslorelin implant. The large variability in the duration of suppression of gonadal activity makes the definition of the optimal time for reimplantation quite challenging. In addition, the temporary stimulation phase occurring in the weeks following deslorelin implantation can induce in adult female cats a fertile estrus that needs to be managed to avoid unwanted pregnancy. Longer duration and larger scale controlled field studies implementing blinding, a negative control group and a carefully controlled randomization to each group are needed. Furthermore, the effects of repeated treatment need to be investigated. Finally, the effect of treatment on growth and bone quality of prepubertal cats needs to be assessed. However, the ease of use, long-lasting effects and reversibility of deslorelin implants are strong positive points supporting their use for controlling feline reproduction. © The Author(s) 2015.

  10. Subsonic flight test evaluation of a performance seeking control algorithm on an F-15 airplane

    NASA Technical Reports Server (NTRS)

    Gilyard, Glenn B.; Orme, John S.

    1992-01-01

    The subsonic flight test evaluation phase of the NASA F-15 (powered by F 100 engines) performance seeking control program was completed for single-engine operation at part- and military-power settings. The subsonic performance seeking control algorithm optimizes the quasi-steady-state performance of the propulsion system for three modes of operation. The minimum fuel flow mode minimizes fuel consumption. The minimum thrust mode maximizes thrust at military power. Decreases in thrust-specific fuel consumption of 1 to 2 percent were measured in the minimum fuel flow mode; these fuel savings are significant, especially for supersonic cruise aircraft. Decreases of up to approximately 100 degree R in fan turbine inlet temperature were measured in the minimum temperature mode. Temperature reductions of this magnitude would more than double turbine life if inlet temperature was the only life factor. Measured thrust increases of up to approximately 15 percent in the maximum thrust mode cause substantial increases in aircraft acceleration. The system dynamics of the closed-loop algorithm operation were good. The subsonic flight phase has validated the performance seeking control technology, which can significantly benefit the next generation of fighter and transport aircraft.

  11. Energy optimization in mobile sensor networks

    NASA Astrophysics Data System (ADS)

    Yu, Shengwei

    Mobile sensor networks are considered to consist of a network of mobile robots, each of which has computation, communication and sensing capabilities. Energy efficiency is a critical issue in mobile sensor networks, especially when mobility (i.e., locomotion control), routing (i.e., communications) and sensing are unique characteristics of mobile robots for energy optimization. This thesis focuses on the problem of energy optimization of mobile robotic sensor networks, and the research results can be extended to energy optimization of a network of mobile robots that monitors the environment, or a team of mobile robots that transports materials from stations to stations in a manufacturing environment. On the energy optimization of mobile robotic sensor networks, our research focuses on the investigation and development of distributed optimization algorithms to exploit the mobility of robotic sensor nodes for network lifetime maximization. In particular, the thesis studies these five problems: 1. Network-lifetime maximization by controlling positions of networked mobile sensor robots based on local information with distributed optimization algorithms; 2. Lifetime maximization of mobile sensor networks with energy harvesting modules; 3. Lifetime maximization using joint design of mobility and routing; 4. Optimal control for network energy minimization; 5. Network lifetime maximization in mobile visual sensor networks. In addressing the first problem, we consider only the mobility strategies of the robotic relay nodes in a mobile sensor network in order to maximize its network lifetime. By using variable substitutions, the original problem is converted into a convex problem, and a variant of the sub-gradient method for saddle-point computation is developed for solving this problem. An optimal solution is obtained by the method. Computer simulations show that mobility of robotic sensors can significantly prolong the lifetime of the whole robotic sensor network while consuming negligible amount of energy for mobility cost. For the second problem, the problem is extended to accommodate mobile robotic nodes with energy harvesting capability, which makes it a non-convex optimization problem. The non-convexity issue is tackled by using the existing sequential convex approximation method, based on which we propose a novel procedure of modified sequential convex approximation that has fast convergence speed. For the third problem, the proposed procedure is used to solve another challenging non-convex problem, which results in utilizing mobility and routing simultaneously in mobile robotic sensor networks to prolong the network lifetime. The results indicate that joint design of mobility and routing has an edge over other methods in prolonging network lifetime, which is also the justification for the use of mobility in mobile sensor networks for energy efficiency purpose. For the fourth problem, we include the dynamics of the robotic nodes in the problem by modeling the networked robotic system using hybrid systems theory. A novel distributed method for the networked hybrid system is used to solve the optimal moving trajectories for robotic nodes and optimal network links, which are not answered by previous approaches. Finally, the fact that mobility is more effective in prolonging network lifetime for a data-intensive network leads us to apply our methods to study mobile visual sensor networks, which are useful in many applications. We investigate the joint design of mobility, data routing, and encoding power to help improving the video quality while maximizing the network lifetime. This study leads to a better understanding of the role mobility can play in data-intensive surveillance sensor networks.

  12. Seismic data enhancement and regularization using finite offset Common Diffraction Surface (CDS) stack

    NASA Astrophysics Data System (ADS)

    Garabito, German; Cruz, João Carlos Ribeiro; Oliva, Pedro Andrés Chira; Söllner, Walter

    2017-01-01

    The Common Reflection Surface stack is a robust method for simulating zero-offset and common-offset sections with high accuracy from multi-coverage seismic data. For simulating common-offset sections, the Common-Reflection-Surface stack method uses a hyperbolic traveltime approximation that depends on five kinematic parameters for each selected sample point of the common-offset section to be simulated. The main challenge of this method is to find a computationally efficient data-driven optimization strategy for accurately determining the five kinematic stacking parameters on which each sample of the stacked common-offset section depends. Several authors have applied multi-step strategies to obtain the optimal parameters by combining different pre-stack data configurations. Recently, other authors used one-step data-driven strategies based on a global optimization for estimating simultaneously the five parameters from multi-midpoint and multi-offset gathers. In order to increase the computational efficiency of the global optimization process, we use in this paper a reduced form of the Common-Reflection-Surface traveltime approximation that depends on only four parameters, the so-called Common Diffraction Surface traveltime approximation. By analyzing the convergence of both objective functions and the data enhancement effect after applying the two traveltime approximations to the Marmousi synthetic dataset and a real land dataset, we conclude that the Common-Diffraction-Surface approximation is more efficient within certain aperture limits and preserves at the same time a high image accuracy. The preserved image quality is also observed in a direct comparison after applying both approximations for simulating common-offset sections on noisy pre-stack data.

  13. Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

    PubMed

    Johnson, Marcus; Kamalapurkar, Rushikesh; Bhasin, Shubhendu; Dixon, Warren E

    2015-08-01

    An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.

  14. Effect of design selection on response surface performance

    NASA Technical Reports Server (NTRS)

    Carpenter, William C.

    1993-01-01

    The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

  15. A temperature-based feedback control system for electromagnetic phased-array hyperthermia: theory and simulation.

    PubMed

    Kowalski, M E; Jin, J M

    2003-03-07

    A hybrid proportional-integral-in-time and cost-minimizing-in-space feedback control system for electromagnetic, deep regional hyperthermia is proposed. The unique features of this controller are that (1) it uses temperature, not specific absorption rate, as the criterion for selecting the relative phases and amplitudes with which to drive the electromagnetic phased-array used for hyperthermia and (2) it requires on-line computations that are all deterministic in duration. The former feature, in addition to optimizing the treatment directly on the basis of a clinically relevant quantity, also allows the controller to sense and react to time- and temperature-dependent changes in local blood perfusion rates and other factors that can significantly impact the temperature distribution quality of the delivered treatment. The latter feature makes it feasible to implement the scheme on-line in a real-time feedback control loop. This is in sharp contrast to other temperature optimization techniques proposed in the literature that generally involve an iterative approximation that cannot be guaranteed to terminate in a fixed amount of computational time. An example of its application is presented to illustrate the properties and demonstrate the capability of the controller to sense and compensate for local, time-dependent changes in blood perfusion rates.

  16. Constrained H1-regularization schemes for diffeomorphic image registration

    PubMed Central

    Mang, Andreas; Biros, George

    2017-01-01

    We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss–)Newton–Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient. PMID:29075361

  17. Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

    NASA Technical Reports Server (NTRS)

    Jardin, Matthew R.

    2004-01-01

    A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

  18. Comparison of some optimal control methods for the design of turbine blades

    NASA Technical Reports Server (NTRS)

    Desilva, B. M. E.; Grant, G. N. C.

    1977-01-01

    This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

  19. A trust region approach with multivariate Padé model for optimal circuit design

    NASA Astrophysics Data System (ADS)

    Abdel-Malek, Hany L.; Ebid, Shaimaa E. K.; Mohamed, Ahmed S. A.

    2017-11-01

    Since the optimization process requires a significant number of consecutive function evaluations, it is recommended to replace the function by an easily evaluated approximation model during the optimization process. The model suggested in this article is based on a multivariate Padé approximation. This model is constructed using data points of ?, where ? is the number of parameters. The model is updated over a sequence of trust regions. This model avoids the slow convergence of linear models of ? and has features of quadratic models that need interpolation data points of ?. The proposed approach is tested by applying it to several benchmark problems. Yield optimization using such a direct method is applied to some practical circuit examples. Minimax solution leads to a suitable initial point to carry out the yield optimization process. The yield is optimized by the proposed derivative-free method for active and passive filter examples.

  20. On optimal infinite impulse response edge detection filters

    NASA Technical Reports Server (NTRS)

    Sarkar, Sudeep; Boyer, Kim L.

    1991-01-01

    The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

  1. Suboptimal Scheduling in Switched Systems With Continuous-Time Dynamics: A Least Squares Approach.

    PubMed

    Sardarmehni, Tohid; Heydari, Ali

    2018-06-01

    Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are presented. The first solution formulates a policy iteration (PI) algorithm for the switched systems with recursive least squares. To reduce the computational burden imposed by the PI algorithm, a second solution, called single loop PI, is presented. Online and concurrent training algorithms are discussed for implementing each solution. At last, effectiveness of the presented algorithms is evaluated through numerical simulations.

  2. A two-step method for developing a control rod program for boiling water reactors

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Taner, M.S.; Levine, S.H.; Hsiao, M.Y.

    1992-01-01

    This paper reports on a two-step method that is established for the generation of a long-term control rod program for boiling water reactors (BWRs). The new method assumes a time-variant target power distribution in core depletion. In the new method, the BWR control rod programming is divided into two steps. In step 1, a sequence of optimal, exposure-dependent Haling power distribution profiles is generated, utilizing the spectral shift concept. In step 2, a set of exposure-dependent control rod patterns is developed by using the Haling profiles generated at step 1 as a target. The new method is implemented in amore » computer program named OCTOPUS. The optimization procedure of OCTOPUS is based on the method of approximation programming, in which the SIMULATE-E code is used to determine the nucleonics characteristics of the reactor core state. In a test in cycle length over a time-invariant, target Haling power distribution case because of a moderate application of spectral shift. No thermal limits of the core were violated. The gain in cycle length could be increased further by broadening the extent of the spetral shift.« less

  3. False Discovery Control in Large-Scale Spatial Multiple Testing

    PubMed Central

    Sun, Wenguang; Reich, Brian J.; Cai, T. Tony; Guindani, Michele; Schwartzman, Armin

    2014-01-01

    Summary This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both point-wise and cluster-wise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate, respectively. A data-driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple testing procedures are asymptotically valid and can be effectively implemented using Bayesian computational algorithms for analysis of large spatial data sets. Numerical results show that the proposed procedures lead to more accurate error control and better power performance than conventional methods. We demonstrate our methods for analyzing the time trends in tropospheric ozone in eastern US. PMID:25642138

  4. Demonstrative fractional order - PID controller based DC motor drive on digital platform.

    PubMed

    Khubalkar, Swapnil W; Junghare, Anjali S; Aware, Mohan V; Chopade, Amit S; Das, Shantanu

    2017-09-21

    In industrial drives applications, fractional order controllers can exhibit phenomenal impact due to realization through digital implementation. Digital fractional order controllers have created wide scope as it possess the inherent advantages like robustness against the plant parameter variation. This paper provides brief design procedure of fractional order proportional-integral-derivative (FO-PID) controller through the indirect approach of approximation using constant phase technique. The new modified dynamic particle swarm optimization (IdPSO) technique is proposed to find controller parameters. The FO-PID controller is implemented using floating point digital signal processor. The building blocks are designed and assembled with all peripheral components for the 1.5kW industrial DC motor drive. The robust operation for parametric variation is ascertained by testing the controller with two separately excited DC motors with the same rating but different parameters. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  5. Variational Gaussian approximation for Poisson data

    NASA Astrophysics Data System (ADS)

    Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

    2018-02-01

    The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

  6. A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Dzielski, John Edward

    1988-01-01

    Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

  7. Direct energy balance based active disturbance rejection control for coal-fired power plant.

    PubMed

    Sun, Li; Hua, Qingsong; Li, Donghai; Pan, Lei; Xue, Yali; Lee, Kwang Y

    2017-09-01

    The conventional direct energy balance (DEB) based PI control can fulfill the fundamental tracking requirements of the coal-fired power plant. However, it is challenging to deal with the cases when the coal quality variation is present. To this end, this paper introduces the active disturbance rejection control (ADRC) to the DEB structure, where the coal quality variation is deemed as a kind of unknown disturbance that can be estimated and mitigated promptly. Firstly, the nonlinearity of a recent power plant model is analyzed based on the gap metric, which provides guidance on how to set the pressure set-point in line with the power demand. Secondly, the approximate decoupling effect of the DEB structure is analyzed based on the relative gain analysis in frequency domain. Finally, the synthesis of the DEB based ADRC control system is carried out based on multi-objective optimization. The optimized ADRC results show that the integrated absolute error (IAE) indices of the tracking performances in both loops can be simultaneously improved, in comparison with the DEB based PI control and H ∞ control system. The regulation performance in the presence of the coal quality variation is significantly improved under the ADRC control scheme. Moreover, the robustness of the proposed strategy is shown comparable with the H ∞ control. Copyright © 2017. Published by Elsevier Ltd.

  8. Behavior sensitivities for control augmented structures

    NASA Technical Reports Server (NTRS)

    Manning, R. A.; Lust, R. V.; Schmit, L. A.

    1987-01-01

    During the past few years it has been recognized that combining passive structural design methods with active control techniques offers the prospect of being able to find substantially improved designs. These developments have stimulated interest in augmenting structural synthesis by adding active control system design variables to those usually considered in structural optimization. An essential step in extending the approximation concepts approach to control augmented structural synthesis is the development of a behavior sensitivity analysis capability for determining rates of change of dynamic response quantities with respect to changes in structural and control system design variables. Behavior sensitivity information is also useful for man-machine interactive design as well as in the context of system identification studies. Behavior sensitivity formulations for both steady state and transient response are presented and the quality of the resulting derivative information is evaluated.

  9. The muscle spindle as a feedback element in muscle control

    NASA Technical Reports Server (NTRS)

    Andrews, L. T.; Iannone, A. M.; Ewing, D. J.

    1973-01-01

    The muscle spindle, the feedback element in the myotatic (stretch) reflex, is a major contributor to muscular control. Therefore, an accurate description of behavior of the muscle spindle during active contraction of the muscle, as well as during passive stretch, is essential to the understanding of muscle control. Animal experiments were performed in order to obtain the data necessary to model the muscle spindle. Spectral density functions were used to identify a linear approximation of the two types of nerve endings from the spindle. A model reference adaptive control system was used on a hybrid computer to optimize the anatomically defined lumped parameter estimate of the spindle. The derived nonlinear model accurately predicts the behavior of the muscle spindle both during active discharge and during its silent period. This model is used to determine the mechanism employed to control muscle movement.

  10. Adaptive control based on retrospective cost optimization

    NASA Technical Reports Server (NTRS)

    Bernstein, Dennis S. (Inventor); Santillo, Mario A. (Inventor)

    2012-01-01

    A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.

  11. Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

    NASA Technical Reports Server (NTRS)

    Carpenter, William C.

    1991-01-01

    Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

  12. Optimal moving grids for time-dependent partial differential equations

    NASA Technical Reports Server (NTRS)

    Wathen, A. J.

    1989-01-01

    Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

  13. Optimal moving grids for time-dependent partial differential equations

    NASA Technical Reports Server (NTRS)

    Wathen, A. J.

    1992-01-01

    Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

  14. Pattern formations and optimal packing.

    PubMed

    Mityushev, Vladimir

    2016-04-01

    Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

  15. Development of a chitosan based double layer-coated tablet as a platform for colon-specific drug delivery

    PubMed Central

    Kim, Min Soo; Yeom, Dong Woo; Kim, Sung Rae; Yoon, Ho Yub; Kim, Chang Hyun; Son, Ho Yong; Kim, Jin Han; Lee, Sangkil; Choi, Young Wook

    2017-01-01

    A double layer-coated colon-specific drug delivery system (DL-CDDS) was developed, which consisted of chitosan (CTN) based polymeric subcoating of the core tablet containing citric acid for microclimate acidification, followed by an enteric coating. The polymeric composition ratio of Eudragit E100 and ethyl cellulose and amount of subcoating were optimized using a two-level factorial design method. Drug-release characteristics in terms of dissolution efficiency and controlled-release duration were evaluated in various dissolution media, such as simulated colonic fluid in the presence or absence of CTNase. Microflora activation and a stepwise mechanism for drug release were postulated. Consequently, the optimized DL-CDDS showed drug release in a controlled manner by inhibiting drug release in the stomach and intestine, but releasing the drug gradually in the colon (approximately 40% at 10 hours and 92% at 24 hours in CTNase-supplemented simulated colonic fluid), indicating its feasibility as a novel platform for CDD. PMID:28053506

  16. Immediate tight sealing of skin incisions using an innovative temperature-controlled laser soldering device: in vivo study in porcine skin.

    PubMed

    Simhon, David; Halpern, Marisa; Brosh, Tamar; Vasilyev, Tamar; Ravid, Avi; Tennenbaum, Tamar; Nevo, Zvi; Katzir, Abraham

    2007-02-01

    A feedback temperature-controlled laser soldering system (TCLS) was used for bonding skin incisions on the backs of pigs. The study was aimed: 1) to characterize the optimal soldering parameters, and 2) to compare the immediate and long-term wound healing outcomes with other wound closure modalities. A TCLS was used to bond the approximated wound margins of skin incisions on porcine backs. The reparative outcomes were evaluated macroscopically, microscopically, and immunohistochemically. The optimal soldering temperature was found to be 65 degrees C and the operating time was significantly shorter than with suturing. The immediate tight sealing of the wound by the TCLS contributed to rapid, high quality wound healing in comparison to Dermabond or Histoacryl cyanoacrylate glues or standard suturing. TCLS of incisions in porcine skin has numerous advantages, including rapid procedure and high quality reparative outcomes, over the common standard wound closure procedures. Further studies with a variety of skin lesions are needed before advocating this technique for clinical use.

  17. Individualized drug dosing using RBF-Galerkin method: Case of anemia management in chronic kidney disease.

    PubMed

    Mirinejad, Hossein; Gaweda, Adam E; Brier, Michael E; Zurada, Jacek M; Inanc, Tamer

    2017-09-01

    Anemia is a common comorbidity in patients with chronic kidney disease (CKD) and is frequently associated with decreased physical component of quality of life, as well as adverse cardiovascular events. Current treatment methods for renal anemia are mostly population-based approaches treating individual patients with a one-size-fits-all model. However, FDA recommendations stipulate individualized anemia treatment with precise control of the hemoglobin concentration and minimal drug utilization. In accordance with these recommendations, this work presents an individualized drug dosing approach to anemia management by leveraging the theory of optimal control. A Multiple Receding Horizon Control (MRHC) approach based on the RBF-Galerkin optimization method is proposed for individualized anemia management in CKD patients. Recently developed by the authors, the RBF-Galerkin method uses the radial basis function approximation along with the Galerkin error projection to solve constrained optimal control problems numerically. The proposed approach is applied to generate optimal dosing recommendations for individual patients. Performance of the proposed approach (MRHC) is compared in silico to that of a population-based anemia management protocol and an individualized multiple model predictive control method for two case scenarios: hemoglobin measurement with and without observational errors. In silico comparison indicates that hemoglobin concentration with MRHC method has less variation among the methods, especially in presence of measurement errors. In addition, the average achieved hemoglobin level from the MRHC is significantly closer to the target hemoglobin than that of the other two methods, according to the analysis of variance (ANOVA) statistical test. Furthermore, drug dosages recommended by the MRHC are more stable and accurate and reach the steady-state value notably faster than those generated by the other two methods. The proposed method is highly efficient for the control of hemoglobin level, yet provides accurate dosage adjustments in the treatment of CKD anemia. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. Active Control of Sound Radiation due to Subsonic Wave Scattering from Discontinuities on Thin Elastic Beams.

    NASA Astrophysics Data System (ADS)

    Guigou, Catherine Renee J.

    1992-01-01

    Much progress has been made in recent years in active control of sound radiation from vibrating structures. Reduction of the far-field acoustic radiation can be obtained by directly modifying the response of the structure by applying structural inputs rather than by adding acoustic sources. Discontinuities, which are present in many structures are often important in terms of sound radiation due to wave scattering behavior at their location. In this thesis, an edge or boundary type discontinuity (clamped edge) and a point discontinuity (blocking mass) are analytically studied in terms of sound radiation. When subsonic vibrational waves impinge on these discontinuities, large scattered sound levels are radiated. Active control is then achieved by applying either control forces, which approximate shakers, or pairs of control moments, which approximate piezoelectric actuators, near the discontinuity. Active control of sound radiation from a simply-supported beam is also examined. For a single frequency, the flexural response of the beam subject to an incident wave or an input force (disturbance) and to control forces or control moments is expressed in terms of waves of both propagating and near-field types. The far-field radiated pressure is then evaluated in terms of the structural response, using Rayleigh's formula or a stationary phase approach, depending upon the application. The control force and control moment magnitudes are determined by optimizing a quadratic cost function, which is directly related to the control performance. On determining the optimal control complex amplitudes, these can be resubstituted in the constitutive equations for the system under study and the minimized radiated fields can be evaluated. High attenuation in radiated sound power and radiated acoustic pressure is found to be possible when one or two active control actuators are located near the discontinuity, as is shown to be mostly associated with local changes in beam response near the discontinuity. The effect of the control actuators on the far-field radiated pressure, the wavenumber spectrum, the flexural displacement and the near-field time averaged intensity and pressure distributions are studied in order to further understand the control mechanisms. The influence of the near-field structural waves is investigated as well. Some experimental results are presented for comparison.

  19. Strategy for pH control and pH feedback-controlled substrate feeding for high-level production of L-tryptophan by Escherichia coli.

    PubMed

    Cheng, Li-Kun; Wang, Jian; Xu, Qing-Yang; Zhao, Chun-Guang; Shen, Zhi-Qiang; Xie, Xi-Xian; Chen, Ning

    2013-05-01

    Optimum production of L-tryptophan by Escherichia coli depends on pH. Here, we established conditions for optimizing the production of L-tryptophan. The optimum pH range was 6.5-7.2, and pH was controlled using a three-stage strategy [pH 6.5 (0-12 h), pH 6.8 (12-24 h), and pH 7.2 (24-38 h)]. Specifically, ammonium hydroxide was used to adjust pH during the initial 24 h, and potassium hydroxide and ammonium hydroxide (1:2, v/v) were used to adjust pH during 24-38 h. Under these conditions, NH4 (+) and K(+) concentrations were kept below the threshold for inhibiting L-tryptophan production. Optimization was also accomplished using ratios (v/v) of glucose to alkali solutions equal to 4:1 (5-24 h) and 6:1 (24-38 h). The concentration of glucose and the pH were controlled by adjusting the pH automatically. Applying a pH-feedback feeding method, the steady-state concentration of glucose was maintained at approximately 0.2 ± 0.02 g/l, and acetic acid accumulated to a concentration of 1.15 ± 0.03 g/l, and the plasmid stability was 98 ± 0.5 %. The final, optimized concentration of L-tryptophan was 43.65 ± 0.29 g/l from 52.43 ± 0.38 g/l dry cell weight.

  20. Optimal control of greenhouse gas emissions and system cost for integrated municipal solid waste management with considering a hierarchical structure.

    PubMed

    Li, Jing; He, Li; Fan, Xing; Chen, Yizhong; Lu, Hongwei

    2017-08-01

    This study presents a synergic optimization of control for greenhouse gas (GHG) emissions and system cost in integrated municipal solid waste (MSW) management on a basis of bi-level programming. The bi-level programming is formulated by integrating minimizations of GHG emissions at the leader level and system cost at the follower level into a general MSW framework. Different from traditional single- or multi-objective approaches, the proposed bi-level programming is capable of not only addressing the tradeoffs but also dealing with the leader-follower relationship between different decision makers, who have dissimilar perspectives interests. GHG emission control is placed at the leader level could emphasize the significant environmental concern in MSW management. A bi-level decision-making process based on satisfactory degree is then suitable for solving highly nonlinear problems with computationally effectiveness. The capabilities and effectiveness of the proposed bi-level programming are illustrated by an application of a MSW management problem in Canada. Results show that the obtained optimal management strategy can bring considerable revenues, approximately from 76 to 97 million dollars. Considering control of GHG emissions, it would give priority to the development of the recycling facility throughout the whole period, especially in latter periods. In terms of capacity, the existing landfill is enough in the future 30 years without development of new landfills, while expansion to the composting and recycling facilities should be paid more attention.

  1. A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes

    NASA Technical Reports Server (NTRS)

    Martin, Rodney Alexander

    2009-01-01

    In many complex engineered systems, the ability to give an alarm prior to impending critical events is of great importance. These critical events may have varying degrees of severity, and in fact they may occur during normal system operation. In this article, we investigate approximations to theoretically optimal methods of designing alarm systems for the prediction of level-crossings by a zero-mean stationary linear dynamic system driven by Gaussian noise. An optimal alarm system is designed to elicit the fewest false alarms for a fixed detection probability. This work introduces the use of Kalman filtering in tandem with the optimal level-crossing problem. It is shown that there is a negligible loss in overall accuracy when using approximations to the theoretically optimal predictor, at the advantage of greatly reduced computational complexity. I

  2. Optimal percolation on multiplex networks.

    PubMed

    Osat, Saeed; Faqeeh, Ali; Radicchi, Filippo

    2017-11-16

    Optimal percolation is the problem of finding the minimal set of nodes whose removal from a network fragments the system into non-extensive disconnected clusters. The solution to this problem is important for strategies of immunization in disease spreading, and influence maximization in opinion dynamics. Optimal percolation has received considerable attention in the context of isolated networks. However, its generalization to multiplex networks has not yet been considered. Here we show that approximating the solution of the optimal percolation problem on a multiplex network with solutions valid for single-layer networks extracted from the multiplex may have serious consequences in the characterization of the true robustness of the system. We reach this conclusion by extending many of the methods for finding approximate solutions of the optimal percolation problem from single-layer to multiplex networks, and performing a systematic analysis on synthetic and real-world multiplex networks.

  3. Approximate optimal guidance for the advanced launch system

    NASA Technical Reports Server (NTRS)

    Feeley, T. S.; Speyer, J. L.

    1993-01-01

    A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

  4. The trust-region self-consistent field method in Kohn-Sham density-functional theory.

    PubMed

    Thøgersen, Lea; Olsen, Jeppe; Köhn, Andreas; Jørgensen, Poul; Sałek, Paweł; Helgaker, Trygve

    2005-08-15

    The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

  5. Effective Clipart Image Vectorization through Direct Optimization of Bezigons.

    PubMed

    Yang, Ming; Chao, Hongyang; Zhang, Chi; Guo, Jun; Yuan, Lu; Sun, Jian

    2016-02-01

    Bezigons, i.e., closed paths composed of Bézier curves, have been widely employed to describe shapes in image vectorization results. However, most existing vectorization techniques infer the bezigons by simply approximating an intermediate vector representation (such as polygons). Consequently, the resultant bezigons are sometimes imperfect due to accumulated errors, fitting ambiguities, and a lack of curve priors, especially for low-resolution images. In this paper, we describe a novel method for vectorizing clipart images. In contrast to previous methods, we directly optimize the bezigons rather than using other intermediate representations; therefore, the resultant bezigons are not only of higher fidelity compared with the original raster image but also more reasonable because they were traced by a proficient expert. To enable such optimization, we have overcome several challenges and have devised a differentiable data energy as well as several curve-based prior terms. To improve the efficiency of the optimization, we also take advantage of the local control property of bezigons and adopt an overlapped piecewise optimization strategy. The experimental results show that our method outperforms both the current state-of-the-art method and commonly used commercial software in terms of bezigon quality.

  6. Improving multi-objective reservoir operation optimization with sensitivity-informed problem decomposition

    NASA Astrophysics Data System (ADS)

    Chu, J. G.; Zhang, C.; Fu, G. T.; Li, Y.; Zhou, H. C.

    2015-04-01

    This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce the computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed problem decomposition dramatically reduces the computational demands required for attaining high quality approximations of optimal tradeoff relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed problem decomposition and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform problem decomposition when solving the complex multi-objective reservoir operation problems.

  7. A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model

    NASA Astrophysics Data System (ADS)

    Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji

    2017-09-01

    This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.

  8. Enhanced production of azadirachtin by hairy root cultures of Azadirachta indica A. Juss by elicitation and media optimization.

    PubMed

    Satdive, Ramesh K; Fulzele, Devanand P; Eapen, Susan

    2007-02-01

    Azadirachtin is one of the most potent biopesticides so far developed from a plant sources. Influence of different culture media and elicitation on growth and production of azadirachtin by hairy root cultures of Azadirachta indica was studied. Out of the three media tested, namely Ohyama and Nitsch, Gamborg's and Murashige and Skoog's basal media, hairy roots cultured on Ohyama and Nitsch's basal medium produced maximum yield of azadirachtin (0.0166% dry weight, DW). Addition of biotic elicitor enhanced the production of azadirachtin by approximately 5-fold (0.074% DW), while signal compounds such as jasmonic acid and salicylic acid showed a approximately 6 (0.095% DW) and approximately 9-fold (0.14% DW) enhancement, respectively, in the production of azadirachtin as compared to control cultures on Ohyama and Nitsch medium. Extracts from hairy roots were found to be superior to those from the leaves for antifeedant activity against the larvae of Spodoptera litura.

  9. A comparison of optimal semi-active suspension systems regarding vehicle ride comfort

    NASA Astrophysics Data System (ADS)

    Koulocheris, Dimitrios; Papaioannou, Georgios; Chrysos, Emmanouil

    2017-10-01

    The aim of this work is to present a comparison of the main semi active suspension systems used in a passenger car, after having optimized the suspension systems of the vehicle model in respect with ride comfort and road holding. Thus, a half car model, equipped with controllable dampers, along with a seat and a driver was implemented. Semi-active suspensions have received a lot of attention since they seem to provide the best compromise between cost (energy consumption, actuators/sensors hardware) and performance in comparison with active and passive suspensions. In this work, the semi active suspension systems studied are comfort oriented and consist of (a) the two version of Skyhook control (two states skyhook and skyhook linear approximation damper), (b) the acceleration driven damper (ADD), (c) the power driven damper (PDD), (d) the combination of Skyhook and ADD (Mixed Skyhook-ADD) and (e) the combination of the two with the use of a sensor. The half car model equipped with the above suspension systems was excited by a road bump, and was optimized using genetic algorithms (GA) in respect with ride comfort and road holding. This study aims to highlight how the optimization of the vehicle model could lead to the best compromise between ride comfort and road holding, overcoming their well-known trade-off. The optimum results were compared with important performance metrics regarding the vehicle’s dynamic behaviour in general.

  10. Design Sensitivity for a Subsonic Aircraft Predicted by Neural Network and Regression Models

    NASA Technical Reports Server (NTRS)

    Hopkins, Dale A.; Patnaik, Surya N.

    2005-01-01

    A preliminary methodology was obtained for the design optimization of a subsonic aircraft by coupling NASA Langley Research Center s Flight Optimization System (FLOPS) with NASA Glenn Research Center s design optimization testbed (COMETBOARDS with regression and neural network analysis approximators). The aircraft modeled can carry 200 passengers at a cruise speed of Mach 0.85 over a range of 2500 n mi and can operate on standard 6000-ft takeoff and landing runways. The design simulation was extended to evaluate the optimal airframe and engine parameters for the subsonic aircraft to operate on nonstandard runways. Regression and neural network approximators were used to examine aircraft operation on runways ranging in length from 4500 to 7500 ft.

  11. Adaptive critic learning techniques for engine torque and air-fuel ratio control.

    PubMed

    Liu, Derong; Javaherian, Hossein; Kovalenko, Olesia; Huang, Ting

    2008-08-01

    A new approach for engine calibration and control is proposed. In this paper, we present our research results on the implementation of adaptive critic designs for self-learning control of automotive engines. A class of adaptive critic designs that can be classified as (model-free) action-dependent heuristic dynamic programming is used in this research project. The goals of the present learning control design for automotive engines include improved performance, reduced emissions, and maintained optimum performance under various operating conditions. Using the data from a test vehicle with a V8 engine, we developed a neural network model of the engine and neural network controllers based on the idea of approximate dynamic programming to achieve optimal control. We have developed and simulated self-learning neural network controllers for both engine torque (TRQ) and exhaust air-fuel ratio (AFR) control. The goal of TRQ control and AFR control is to track the commanded values. For both control problems, excellent neural network controller transient performance has been achieved.

  12. Real-time discrete suboptimal control for systems with input and state delays: Experimental tests on a dehydration process.

    PubMed

    Rodríguez-Guerrero, Liliam; Santos-Sánchez, Omar-Jacobo; Cervantes-Escorcia, Nicolás; Romero, Hugo

    2017-11-01

    This article presents a suboptimal control strategy with finite horizon for affine nonlinear discrete systems with both state and input delays. The Dynamic Programming Approach is used to obtain the suboptimal control sequence, but in order to avoid the computation of the Bellman functional, a numerical approximation of this function is proposed in every step. The feasibility of our proposal is demonstrated via an experimental test on a dehydration process and the obtained results show a good performance and behavior of this process. Then in order to demonstrate the benefits of using this kind of control strategy, the results are compared with a non optimal control strategy, particularly with respect to results produced by an industrial Proportional Integral Derivative (PID) Honeywell controller, which is tuned using the Ziegler-Nichols method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  13. Robust Approximations to the Non-Null Distribution of the Product Moment Correlation Coefficient I: The Phi Coefficient.

    ERIC Educational Resources Information Center

    Edwards, Lynne K.; Meyers, Sarah A.

    Correlation coefficients are frequently reported in educational and psychological research. The robustness properties and optimality among practical approximations when phi does not equal 0 with moderate sample sizes are not well documented. Three major approximations and their variations are examined: (1) a normal approximation of Fisher's Z,…

  14. Laser micropolishing of AISI 304 stainless steel surfaces for cleanability and bacteria removal capability

    NASA Astrophysics Data System (ADS)

    De Giorgi, Chiara; Furlan, Valentina; Demir, Ali Gökhan; Tallarita, Elena; Candiani, Gabriele; Previtali, Barbara

    2017-06-01

    In this work, laser micropolishing (LμP) was employed to reduce the surface roughness and waviness of cold-rolled AISI 304 stainless steel sheets. A pulsed fibre laser operating in the ns regime was used and the influence of laser parameters in a N2-controlled atmospheres was evaluated. In the optimal conditions, the surface remelting induced by the process allowed to reduce the surface roughness by closing cracks and defects formed during the rolling process. Other conditions that did not improve the surface quality were analysed for defect typology. Moreover, laser treatments allowed the production of more hydrophobic surfaces, and no surface chemistry modification was identified. Surface cleanability was investigated with Escherichia coli (E. coli), evaluating the number of residual bacteria adhering to the substrate after a washing procedure. These results showed that LμP is a suitable way to lower the average surface roughness by about 58% and average surface waviness by approximately 38%. The LμP process proved to be effective on the bacteria cleanability as approximately five times fewer bacteria remained on the surfaces treated with the optimized LμP parameters compared to the untreated surfaces.

  15. Reinforcement learning for partially observable dynamic processes: adaptive dynamic programming using measured output data.

    PubMed

    Lewis, F L; Vamvoudakis, Kyriakos G

    2011-02-01

    Approximate dynamic programming (ADP) is a class of reinforcement learning methods that have shown their importance in a variety of applications, including feedback control of dynamical systems. ADP generally requires full information about the system internal states, which is usually not available in practical situations. In this paper, we show how to implement ADP methods using only measured input/output data from the system. Linear dynamical systems with deterministic behavior are considered herein, which are systems of great interest in the control system community. In control system theory, these types of methods are referred to as output feedback (OPFB). The stochastic equivalent of the systems dealt with in this paper is a class of partially observable Markov decision processes. We develop both policy iteration and value iteration algorithms that converge to an optimal controller that requires only OPFB. It is shown that, similar to Q -learning, the new methods have the important advantage that knowledge of the system dynamics is not needed for the implementation of these learning algorithms or for the OPFB control. Only the order of the system, as well as an upper bound on its "observability index," must be known. The learned OPFB controller is in the form of a polynomial autoregressive moving-average controller that has equivalent performance with the optimal state variable feedback gain.

  16. Graphical models for optimal power flow

    DOE PAGES

    Dvijotham, Krishnamurthy; Chertkov, Michael; Van Hentenryck, Pascal; ...

    2016-09-13

    Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithmmore » for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.« less

  17. Alternative derivation of an exchange-only density-functional optimized effective potential

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Joubert, D. P.

    2007-10-15

    An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock-common energy denominator Green's function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Goerling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term canmore » be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r{sup 4} for large r.« less

  18. Alternative derivation of an exchange-only density-functional optimized effective potential

    NASA Astrophysics Data System (ADS)

    Joubert, D. P.

    2007-10-01

    An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock common energy denominator Green’s function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Görling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term can be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r4 for large r .

  19. Parameter Optimization of Pseudo-Rigid-Body Models of MRI-Actuated Catheters

    PubMed Central

    Greigarn, Tipakorn; Liu, Taoming; Çavuşoğlu, M. Cenk

    2016-01-01

    Simulation and control of a system containing compliant mechanisms such as cardiac catheters often incur high computational costs. One way to reduce the costs is to approximate the mechanisms with Pseudo-Rigid-Body Models (PRBMs). A PRBM generally consists of rigid links connected by spring-loaded revolute joints. The lengths of the rigid links and the stiffnesses of the springs are usually chosen to minimize the tip deflection differences between the PRBM and the compliant mechanism. In most applications, only the relationship between end load and tip deflection is considered. This is obviously not applicable for MRI-actuated catheters which is actuated by the coils attached to the body. This paper generalizes PRBM parameter optimization to include loading and reference points along the body. PMID:28261009

  20. Wiener-Hopf optimal control of a hydraulic canal prototype with fractional order dynamics.

    PubMed

    Feliu-Batlle, Vicente; Feliu-Talegón, Daniel; San-Millan, Andres; Rivas-Pérez, Raúl

    2017-06-26

    This article addresses the control of a laboratory hydraulic canal prototype that has fractional order dynamics and a time delay. Controlling this prototype is relevant since its dynamics closely resembles the dynamics of real main irrigation canals. Moreover, the dynamics of hydraulic canals vary largely when the operation regime changes since they are strongly nonlinear systems. All this makes difficult to design adequate controllers. The controller proposed in this article looks for a good time response to step commands. The design criterium for this controller is minimizing the integral performance index ISE. Then a new methodology to control fractional order processes with a time delay, based on the Wiener-Hopf control and the Padé approximation of the time delay, is developed. Moreover, in order to improve the robustness of the control system, a gain scheduling fractional order controller is proposed. Experiments show the adequate performance of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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