Sample records for optimal control problem

  1. Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

    NASA Astrophysics Data System (ADS)

    Kmet', Tibor; Kmet'ová, Mária

    2009-09-01

    A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

  2. 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

  3. Numerical optimization methods for controlled systems with parameters

    NASA Astrophysics Data System (ADS)

    Tyatyushkin, A. I.

    2017-10-01

    First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton's method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

  4. The optimal location of piezoelectric actuators and sensors for vibration control of plates

    NASA Astrophysics Data System (ADS)

    Kumar, K. Ramesh; Narayanan, S.

    2007-12-01

    This paper considers the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQR performance is taken as objective for finding the optimal location of sensor-actuator pairs. The problem is formulated using the finite element method (FEM) as multi-input-multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero-one optimization problem. A genetic algorithm (GA) is used to solve the zero-one optimization problem. Different classical control strategies like direct proportional feedback, constant-gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness.

  5. Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

    NASA Astrophysics Data System (ADS)

    Postnov, Sergey

    2017-11-01

    Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

  6. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1989-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  7. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1990-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  8. Weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1991-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  9. Time-domain finite elements in optimal control with application to launch-vehicle guidance. PhD. Thesis

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.

    1991-01-01

    A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

  10. 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.

  11. 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.

  12. 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.

  13. The design of multirate digital control systems

    NASA Technical Reports Server (NTRS)

    Berg, M. C.

    1986-01-01

    The successive loop closures synthesis method is the only method for multirate (MR) synthesis in common use. A new method for MR synthesis is introduced which requires a gradient-search solution to a constrained optimization problem. Some advantages of this method are that the control laws for all control loops are synthesized simultaneously, taking full advantage of all cross-coupling effects, and that simple, low-order compensator structures are easily accomodated. The algorithm and associated computer program for solving the constrained optimization problem are described. The successive loop closures , optimal control, and constrained optimization synthesis methods are applied to two example design problems. A series of compensator pairs are synthesized for each example problem. The succesive loop closure, optimal control, and constrained optimization synthesis methods are compared, in the context of the two design problems.

  14. On a distinctive feature of problems of calculating time-average characteristics of nuclear reactor optimal control sets

    NASA Astrophysics Data System (ADS)

    Trifonenkov, A. V.; Trifonenkov, V. P.

    2017-01-01

    This article deals with a feature of problems of calculating time-average characteristics of nuclear reactor optimal control sets. The operation of a nuclear reactor during threatened period is considered. The optimal control search problem is analysed. The xenon poisoning causes limitations on the variety of statements of the problem of calculating time-average characteristics of a set of optimal reactor power off controls. The level of xenon poisoning is limited. There is a problem of choosing an appropriate segment of the time axis to ensure that optimal control problem is consistent. Two procedures of estimation of the duration of this segment are considered. Two estimations as functions of the xenon limitation were plot. Boundaries of the interval of averaging are defined more precisely.

  15. Fast Optimization for Aircraft Descent and Approach Trajectory

    NASA Technical Reports Server (NTRS)

    Luchinsky, Dmitry G.; Schuet, Stefan; Brenton, J.; Timucin, Dogan; Smith, David; Kaneshige, John

    2017-01-01

    We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

  16. Optimal control of a harmonic oscillator: Economic interpretations

    NASA Astrophysics Data System (ADS)

    Janová, Jitka; Hampel, David

    2013-10-01

    Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.

  17. 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.

  18. Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

    NASA Astrophysics Data System (ADS)

    Bulgakov, V. K.; Strigunov, V. V.

    2009-05-01

    The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

  19. Dynamic malware containment under an epidemic model with alert

    NASA Astrophysics Data System (ADS)

    Zhang, Tianrui; Yang, Lu-Xing; Yang, Xiaofan; Wu, Yingbo; Tang, Yuan Yan

    2017-03-01

    Alerting at the early stage of malware invasion turns out to be an important complement to malware detection and elimination. This paper addresses the issue of how to dynamically contain the prevalence of malware at a lower cost, provided alerting is feasible. A controlled epidemic model with alert is established, and an optimal control problem based on the epidemic model is formulated. The optimality system for the optimal control problem is derived. The structure of an optimal control for the proposed optimal control problem is characterized under some conditions. Numerical examples show that the cost-efficiency of an optimal control strategy can be enhanced by adjusting the upper and lower bounds on admissible controls.

  20. Optimal Control Problems with Switching Points. Ph.D. Thesis, 1990 Final Report

    NASA Technical Reports Server (NTRS)

    Seywald, Hans

    1991-01-01

    The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

  1. Closed-Loop Optimal Control Implementations for Space Applications

    DTIC Science & Technology

    2016-12-01

    analyses of a series of optimal control problems, several real- time optimal control algorithms are developed that continuously adapt to feedback on the...through the analyses of a series of optimal control problems, several real- time optimal control algorithms are developed that continuously adapt to...information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering

  2. Optimal control of LQR for discrete time-varying systems with input delays

    NASA Astrophysics Data System (ADS)

    Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

    2018-04-01

    In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

  3. Control of Finite-State, Finite Memory Stochastic Systems

    NASA Technical Reports Server (NTRS)

    Sandell, Nils R.

    1974-01-01

    A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

  4. Discrete-time entropy formulation of optimal and adaptive control problems

    NASA Technical Reports Server (NTRS)

    Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.

    1992-01-01

    The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

  5. Mixed-Strategy Chance Constrained Optimal Control

    NASA Technical Reports Server (NTRS)

    Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J.

    2013-01-01

    This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

  6. A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

    NASA Astrophysics Data System (ADS)

    Heinkenschloss, Matthias

    2005-01-01

    We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

  7. Near-Optimal Guidance Method for Maximizing the Reachable Domain of Gliding Aircraft

    NASA Astrophysics Data System (ADS)

    Tsuchiya, Takeshi

    This paper proposes a guidance method for gliding aircraft by using onboard computers to calculate a near-optimal trajectory in real-time, and thereby expanding the reachable domain. The results are applicable to advanced aircraft and future space transportation systems that require high safety. The calculation load of the optimal control problem that is used to maximize the reachable domain is too large for current computers to calculate in real-time. Thus the optimal control problem is divided into two problems: a gliding distance maximization problem in which the aircraft motion is limited to a vertical plane, and an optimal turning flight problem in a horizontal direction. First, the former problem is solved using a shooting method. It can be solved easily because its scale is smaller than that of the original problem, and because some of the features of the optimal solution are obtained in the first part of this paper. Next, in the latter problem, the optimal bank angle is computed from the solution of the former; this is an analytical computation, rather than an iterative computation. Finally, the reachable domain obtained from the proposed near-optimal guidance method is compared with that obtained from the original optimal control problem.

  8. A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

    DOE PAGES

    Molzahn, Daniel K.; Dorfler, Florian K.; Sandberg, Henrik; ...

    2017-07-25

    Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. Here, this paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

  9. A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

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

    Molzahn, Daniel K.; Dorfler, Florian K.; Sandberg, Henrik

    Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. Here, this paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

  10. Optimal Control for Stochastic Delay Evolution Equations

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

    Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

    2016-08-15

    In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

  11. Control problem for a system of linear loaded differential equations

    NASA Astrophysics Data System (ADS)

    Barseghyan, V. R.; Barseghyan, T. V.

    2018-04-01

    The problem of control and optimal control for a system of linear loaded differential equations is considered. Necessary and sufficient conditions for complete controllability and conditions for the existence of a program control and the corresponding motion are formulated. The explicit form of control action for the control problem is constructed and a method for solving the problem of optimal control is proposed.

  12. 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.

  13. 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.

  14. A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems.

    PubMed

    Liu, Ping; Li, Guodong; Liu, Xinggao; Xiao, Long; Wang, Yalin; Yang, Chunhua; Gui, Weihua

    2018-02-01

    High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost; meanwhile, the control quality is efficiently improved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  15. An optimization method for the problems of thermal cloaking of material bodies

    NASA Astrophysics Data System (ADS)

    Alekseev, G. V.; Levin, V. A.

    2016-11-01

    Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

  16. Disturbance decoupling, decentralized control and the Riccati equation

    NASA Technical Reports Server (NTRS)

    Garzia, M. R.; Loparo, K. A.; Martin, C. F.

    1981-01-01

    The disturbance decoupling and optimal decentralized control problems are looked at using identical mathematical techniques. A statement of the problems and the development of their solution approach is presented. Preliminary results are given for the optimal decentralized control problem.

  17. Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

    NASA Astrophysics Data System (ADS)

    Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

    2017-09-01

    This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

  18. A survey of methods of feasible directions for the solution of optimal control problems

    NASA Technical Reports Server (NTRS)

    Polak, E.

    1972-01-01

    Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

  19. An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

    NASA Technical Reports Server (NTRS)

    Lu, Ping

    1992-01-01

    The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

  20. 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.

  1. 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.

  2. Robust Neighboring Optimal Guidance for the Advanced Launch System

    NASA Technical Reports Server (NTRS)

    Hull, David G.

    1993-01-01

    In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

  3. Control and System Theory, Optimization, Inverse and Ill-Posed Problems

    DTIC Science & Technology

    1988-09-14

    Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

  4. Recursive multibody dynamics and discrete-time optimal control

    NASA Technical Reports Server (NTRS)

    Deleuterio, G. M. T.; Damaren, C. J.

    1989-01-01

    A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.

  5. Guidance and control strategies for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Naidu, Desineni S.; Hibey, Joseph L.

    1989-01-01

    The optimal control problem arising in coplanar orbital transfer employing aeroassist technology and the fuel-optimal control problem arising in orbital transfer vehicles employing aeroassist technology are addressed.

  6. A Transformation Approach to Optimal Control Problems with Bounded State Variables

    NASA Technical Reports Server (NTRS)

    Hanafy, Lawrence Hanafy

    1971-01-01

    A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

  7. Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

    NASA Technical Reports Server (NTRS)

    Chen, Guanrong

    1991-01-01

    An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

  8. Multi-step optimization strategy for fuel-optimal orbital transfer of low-thrust spacecraft

    NASA Astrophysics Data System (ADS)

    Rasotto, M.; Armellin, R.; Di Lizia, P.

    2016-03-01

    An effective method for the design of fuel-optimal transfers in two- and three-body dynamics is presented. The optimal control problem is formulated using calculus of variation and primer vector theory. This leads to a multi-point boundary value problem (MPBVP), characterized by complex inner constraints and a discontinuous thrust profile. The first issue is addressed by embedding the MPBVP in a parametric optimization problem, thus allowing a simplification of the set of transversality constraints. The second problem is solved by representing the discontinuous control function by a smooth function depending on a continuation parameter. The resulting trajectory optimization method can deal with different intermediate conditions, and no a priori knowledge of the control structure is required. Test cases in both the two- and three-body dynamics show the capability of the method in solving complex trajectory design problems.

  9. An historical survey of computational methods in optimal control.

    NASA Technical Reports Server (NTRS)

    Polak, E.

    1973-01-01

    Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

  10. 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.

  11. Singular optimal control and the identically non-regular problem in the calculus of variations

    NASA Technical Reports Server (NTRS)

    Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.

    1985-01-01

    A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.

  12. 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.

  13. Optimal Control of Evolution Mixed Variational Inclusions

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

    Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

    2013-12-15

    Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

  14. Geometric versus numerical optimal control of a dissipative spin-(1/2) particle

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

    Lapert, M.; Sugny, D.; Zhang, Y.

    2010-12-15

    We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.

  15. Optimal birth control of age-dependent competitive species III. Overtaking problem

    NASA Astrophysics Data System (ADS)

    He, Ze-Rong; Cheng, Ji-Shu; Zhang, Chun-Guo

    2008-01-01

    A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.

  16. Verification and Optimal Control of Context-Sensitive Probabilistic Boolean Networks Using Model Checking and Polynomial Optimization

    PubMed Central

    Hiraishi, Kunihiko

    2014-01-01

    One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs. PMID:24587766

  17. 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

  18. Optimal reorientation of asymmetric underactuated spacecraft using differential flatness and receding horizon control

    NASA Astrophysics Data System (ADS)

    Cai, Wei-wei; Yang, Le-ping; Zhu, Yan-wei

    2015-01-01

    This paper presents a novel method integrating nominal trajectory optimization and tracking for the reorientation control of an underactuated spacecraft with only two available control torque inputs. By employing a pseudo input along the uncontrolled axis, the flatness property of a general underactuated spacecraft is extended explicitly, by which the reorientation trajectory optimization problem is formulated into the flat output space with all the differential constraints eliminated. Ultimately, the flat output optimization problem is transformed into a nonlinear programming problem via the Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques to overcome the side effects of the differential matrix's ill-conditions on numerical accuracy. Treating the trajectory tracking control as a state regulation problem, we develop a robust closed-loop tracking control law using the receding-horizon control method, and compute the feedback control at each control cycle rapidly via the differential transformation method. Numerical simulation results show that the proposed control scheme is feasible and effective for the reorientation maneuver.

  19. 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.

  20. 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

  1. Parameter meta-optimization of metaheuristics of solving specific NP-hard facility location problem

    NASA Astrophysics Data System (ADS)

    Skakov, E. S.; Malysh, V. N.

    2018-03-01

    The aim of the work is to create an evolutionary method for optimizing the values of the control parameters of metaheuristics of solving the NP-hard facility location problem. A system analysis of the tuning process of optimization algorithms parameters is carried out. The problem of finding the parameters of a metaheuristic algorithm is formulated as a meta-optimization problem. Evolutionary metaheuristic has been chosen to perform the task of meta-optimization. Thus, the approach proposed in this work can be called “meta-metaheuristic”. Computational experiment proving the effectiveness of the procedure of tuning the control parameters of metaheuristics has been performed.

  2. Numerical solution of a conspicuous consumption model with constant control delay☆

    PubMed Central

    Huschto, Tony; Feichtinger, Gustav; Hartl, Richard F.; Kort, Peter M.; Sager, Sebastian; Seidl, Andrea

    2011-01-01

    We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account. This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions. Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case. PMID:22267871

  3. COPS: Large-scale nonlinearly constrained optimization problems

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

    Bondarenko, A.S.; Bortz, D.M.; More, J.J.

    2000-02-10

    The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

  4. A dual method for optimal control problems with initial and final boundary constraints.

    NASA Technical Reports Server (NTRS)

    Pironneau, O.; Polak, E.

    1973-01-01

    This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

  5. Free terminal time optimal control problem of an HIV model based on a conjugate gradient method.

    PubMed

    Jang, Taesoo; Kwon, Hee-Dae; Lee, Jeehyun

    2011-10-01

    The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.

  6. Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

    NASA Astrophysics Data System (ADS)

    Chandra, Rishabh

    Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

  7. An optimal control strategy for hybrid actuator systems: Application to an artificial muscle with electric motor assist.

    PubMed

    Ishihara, Koji; Morimoto, Jun

    2018-03-01

    Humans use multiple muscles to generate such joint movements as an elbow motion. With multiple lightweight and compliant actuators, joint movements can also be efficiently generated. Similarly, robots can use multiple actuators to efficiently generate a one degree of freedom movement. For this movement, the desired joint torque must be properly distributed to each actuator. One approach to cope with this torque distribution problem is an optimal control method. However, solving the optimal control problem at each control time step has not been deemed a practical approach due to its large computational burden. In this paper, we propose a computationally efficient method to derive an optimal control strategy for a hybrid actuation system composed of multiple actuators, where each actuator has different dynamical properties. We investigated a singularly perturbed system of the hybrid actuator model that subdivided the original large-scale control problem into smaller subproblems so that the optimal control outputs for each actuator can be derived at each control time step and applied our proposed method to our pneumatic-electric hybrid actuator system. Our method derived a torque distribution strategy for the hybrid actuator by dealing with the difficulty of solving real-time optimal control problems. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

  8. Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

    NASA Technical Reports Server (NTRS)

    Mook, D. J.; Lew, Jiann-Shiun

    1991-01-01

    Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

  9. Asymptotically suboptimal control of weakly interconnected dynamical systems

    NASA Astrophysics Data System (ADS)

    Dmitruk, N. M.; Kalinin, A. I.

    2016-10-01

    Optimal control problems for a group of systems with weak dynamical interconnections between its constituent subsystems are considered. A method for decentralized control is proposed which distributes the control actions between several controllers calculating in real time control inputs only for theirs subsystems based on the solution of the local optimal control problem. The local problem is solved by asymptotic methods that employ the representation of the weak interconnection by a small parameter. Combination of decentralized control and asymptotic methods allows to significantly reduce the dimension of the problems that have to be solved in the course of the control process.

  10. Dynamics and control of DNA sequence amplification

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

    Marimuthu, Karthikeyan; Chakrabarti, Raj, E-mail: raj@pmc-group.com, E-mail: rajc@andrew.cmu.edu; Division of Fundamental Research, PMC Advanced Technology, Mount Laurel, New Jersey 08054

    2014-10-28

    DNA amplification is the process of replication of a specified DNA sequence in vitro through time-dependent manipulation of its external environment. A theoretical framework for determination of the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is presented based on first-principles biophysical modeling and control theory. Amplification of DNA is formulated as a problem in control theory with optimal solutions that can differ considerably from strategies typically used in practice. Using the Polymerase Chain Reaction as an example, sequence-dependent biophysical models for DNA amplification are cast as control systems, wherein the dynamics of the reactionmore » are controlled by a manipulated input variable. Using these control systems, we demonstrate that there exists an optimal temperature cycling strategy for geometric amplification of any DNA sequence and formulate optimal control problems that can be used to derive the optimal temperature profile. Strategies for the optimal synthesis of the DNA amplification control trajectory are proposed. Analogous methods can be used to formulate control problems for more advanced amplification objectives corresponding to the design of new types of DNA amplification reactions.« less

  11. 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.

  12. Hybrid switched time-optimal control of underactuated spacecraft

    NASA Astrophysics Data System (ADS)

    Olivares, Alberto; Staffetti, Ernesto

    2018-04-01

    This paper studies the time-optimal control problem for an underactuated rigid spacecraft equipped with both reaction wheels and gas jet thrusters that generate control torques about two of the principal axes of the spacecraft. Since a spacecraft equipped with two reaction wheels is not controllable, whereas a spacecraft equipped with two gas jet thrusters is controllable, this mixed actuation ensures controllability in the case in which one of the control axes is unactuated. A novel control logic is proposed for this hybrid actuation in which the reaction wheels are the main actuators and the gas jet thrusters act only after saturation or anticipating future saturation of the reaction wheels. The presence of both reaction wheels and gas jet thrusters gives rise to two operating modes for each actuated axis and therefore the spacecraft can be regarded as a switched dynamical system. The time-optimal control problem for this system is reformulated using the so-called embedding technique and the resulting problem is a classical optimal control problem. The main advantages of this technique are that integer or binary variables do not have to be introduced to model switching decisions between modes and that assumptions about the number of switches are not necessary. It is shown in this paper that this general method for the solution of optimal control problems for switched dynamical systems can efficiently deal with time-optimal control of an underactuated rigid spacecraft in which bound constraints on the torque of the actuators and on the angular momentum of the reaction wheels are taken into account.

  13. Two neural network algorithms for designing optimal terminal controllers with open final time

    NASA Technical Reports Server (NTRS)

    Plumer, Edward S.

    1992-01-01

    Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

  14. Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

    NASA Astrophysics Data System (ADS)

    Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

    2012-03-01

    This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

  15. A sequential linear optimization approach for controller design

    NASA Technical Reports Server (NTRS)

    Horta, L. G.; Juang, J.-N.; Junkins, J. L.

    1985-01-01

    A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

  16. Solving quantum optimal control problems using Clebsch variables and Lin constraints

    NASA Astrophysics Data System (ADS)

    Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

    2018-01-01

    Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

  17. Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

    NASA Astrophysics Data System (ADS)

    Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

    2014-07-01

    We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

  18. An optimal control strategies using vaccination and fogging in dengue fever transmission model

    NASA Astrophysics Data System (ADS)

    Fitria, Irma; Winarni, Pancahayani, Sigit; Subchan

    2017-08-01

    This paper discussed regarding a model and an optimal control problem of dengue fever transmission. We classified the model as human and vector (mosquito) population classes. For the human population, there are three subclasses, such as susceptible, infected, and resistant classes. Then, for the vector population, we divided it into wiggler, susceptible, and infected vector classes. Thus, the model consists of six dynamic equations. To minimize the number of dengue fever cases, we designed two optimal control variables in the model, the giving of fogging and vaccination. The objective function of this optimal control problem is to minimize the number of infected human population, the number of vector, and the cost of the controlling efforts. By giving the fogging optimally, the number of vector can be minimized. In this case, we considered the giving of vaccination as a control variable because it is one of the efforts that are being developed to reduce the spreading of dengue fever. We used Pontryagin Minimum Principle to solve the optimal control problem. Furthermore, the numerical simulation results are given to show the effect of the optimal control strategies in order to minimize the epidemic of dengue fever.

  19. Finite element solution of optimal control problems with state-control inequality constraints

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.

    1992-01-01

    It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

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

    Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

    This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

  1. Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models.

    PubMed

    Sánchez, Helem Sabina; Padula, Fabrizio; Visioli, Antonio; Vilanova, Ramon

    2017-01-01

    In this paper a set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed. The control problem of minimizing at once the integrated absolute error for both the set-point and the load disturbance responses is addressed. The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model subject to a robustness, maximum sensitivity based, constraint has been considered. A set of Pareto optimal solutions is obtained for different normalized dead times and then the optimal balance between the competing objectives is obtained by choosing the Nash solution among the Pareto-optimal ones. A curve fitting procedure has then been applied in order to generate suitable tuning rules. Several simulation results show the effectiveness of the proposed approach. Copyright © 2016. Published by Elsevier Ltd.

  2. 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.

  3. Improved Sensitivity Relations in State Constrained Optimal Control

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

    Bettiol, Piernicola, E-mail: piernicola.bettiol@univ-brest.fr; Frankowska, Hélène, E-mail: frankowska@math.jussieu.fr; Vinter, Richard B., E-mail: r.vinter@imperial.ac.uk

    2015-04-15

    Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjointmore » state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.« less

  4. LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

    NASA Technical Reports Server (NTRS)

    Swei, Sean S.M.; Ayoubi, Mohammad A.

    2017-01-01

    This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

  5. 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.

  6. Control optimization, stabilization and computer algorithms for aircraft applications

    NASA Technical Reports Server (NTRS)

    1975-01-01

    Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

    NASA Astrophysics Data System (ADS)

    Zeb, Anwar; Zaman, Gul; Jung, Il Hyo; Khan, Madad

    2014-06-01

    This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

  12. 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.

  13. 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.

  14. Comparative study of flare control laws. [optimal control of b-737 aircraft approach and landing

    NASA Technical Reports Server (NTRS)

    Nadkarni, A. A.; Breedlove, W. J., Jr.

    1979-01-01

    A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.

  15. Optimal Decentralized Protocol for Electric Vehicle Charging

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

    Gan, LW; Topcu, U; Low, SH

    We propose a decentralized algorithm to optimally schedule electric vehicle (EV) charging. The algorithm exploits the elasticity of electric vehicle loads to fill the valleys in electric load profiles. We first formulate the EV charging scheduling problem as an optimal control problem, whose objective is to impose a generalized notion of valley-filling, and study properties of optimal charging profiles. We then give a decentralized algorithm to iteratively solve the optimal control problem. In each iteration, EVs update their charging profiles according to the control signal broadcast by the utility company, and the utility company alters the control signal to guidemore » their updates. The algorithm converges to optimal charging profiles (that are as "flat" as they can possibly be) irrespective of the specifications (e.g., maximum charging rate and deadline) of EVs, even if EVs do not necessarily update their charging profiles in every iteration, and use potentially outdated control signal when they update. Moreover, the algorithm only requires each EV solving its local problem, hence its implementation requires low computation capability. We also extend the algorithm to track a given load profile and to real-time implementation.« less

  16. Multi-Objective Trajectory Optimization of a Hypersonic Reconnaissance Vehicle with Temperature Constraints

    NASA Astrophysics Data System (ADS)

    Masternak, Tadeusz J.

    This research determines temperature-constrained optimal trajectories for a scramjet-based hypersonic reconnaissance vehicle by developing an optimal control formulation and solving it using a variable order Gauss-Radau quadrature collocation method with a Non-Linear Programming (NLP) solver. The vehicle is assumed to be an air-breathing reconnaissance aircraft that has specified takeoff/landing locations, airborne refueling constraints, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom scramjet aircraft model is adapted from previous work and includes flight dynamics, aerodynamics, and thermal constraints. Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and coverage of high-value targets. To solve the optimal control formulation, a MATLAB-based package called General Pseudospectral Optimal Control Software (GPOPS-II) is used, which transcribes continuous time optimal control problems into an NLP problem. In addition, since a mission profile can have varying vehicle dynamics and en-route imposed constraints, the optimal control problem formulation can be broken up into several "phases" with differing dynamics and/or varying initial/final constraints. Optimal trajectories are developed using several different performance costs in the optimal control formulation: minimum time, minimum time with control penalties, and maximum range. The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for larger-scale operational and campaign planning and execution.

  17. Optimal control for Malaria disease through vaccination

    NASA Astrophysics Data System (ADS)

    Munzir, Said; Nasir, Muhammad; Ramli, Marwan

    2018-01-01

    Malaria is a disease caused by an amoeba (single-celled animal) type of plasmodium where anopheles mosquito serves as the carrier. This study examines the optimal control problem of malaria disease spread based on Aron and May (1982) SIR type models and seeks the optimal solution by minimizing the prevention of the spreading of malaria by vaccine. The aim is to investigate optimal control strategies on preventing the spread of malaria by vaccination. The problem in this research is solved using analytical approach. The analytical method uses the Pontryagin Minimum Principle with the symbolic help of MATLAB software to obtain optimal control result and to analyse the spread of malaria with vaccination control.

  18. Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

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

    Gariboldi, C.; E-mail: cgariboldi@exa.unrc.edu.ar; Tarzia, D.

    2003-05-21

    We consider a steady-state heat conduction problem P{sub {alpha}} with mixed boundary conditions for the Poisson equation depending on a positive parameter {alpha} , which represents the heat transfer coefficient on a portion {gamma} {sub 1} of the boundary of a given bounded domain in R{sup n} . We formulate distributed optimal control problems over the internal energy g for each {alpha}. We prove that the optimal control g{sub o}p{sub {alpha}} and its corresponding system u{sub go}p{sub {alpha}}{sub {alpha}} and adjoint p{sub go}p{sub {alpha}}{sub {alpha}} states for each {alpha} are strongly convergent to g{sub op},u{sub gop} and p{sub gop} ,more » respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion {gamma}{sub 1} . We use the fixed point and elliptic variational inequality theories.« less

  19. Deterministic methods for multi-control fuel loading optimization

    NASA Astrophysics Data System (ADS)

    Rahman, Fariz B. Abdul

    We have developed a multi-control fuel loading optimization code for pressurized water reactors based on deterministic methods. The objective is to flatten the fuel burnup profile, which maximizes overall energy production. The optimal control problem is formulated using the method of Lagrange multipliers and the direct adjoining approach for treatment of the inequality power peaking constraint. The optimality conditions are derived for a multi-dimensional multi-group optimal control problem via calculus of variations. Due to the Hamiltonian having a linear control, our optimal control problem is solved using the gradient method to minimize the Hamiltonian and a Newton step formulation to obtain the optimal control. We are able to satisfy the power peaking constraint during depletion with the control at beginning of cycle (BOC) by building the proper burnup path forward in time and utilizing the adjoint burnup to propagate the information back to the BOC. Our test results show that we are able to achieve our objective and satisfy the power peaking constraint during depletion using either the fissile enrichment or burnable poison as the control. Our fuel loading designs show an increase of 7.8 equivalent full power days (EFPDs) in cycle length compared with 517.4 EFPDs for the AP600 first cycle.

  20. Efficient computation of optimal actions.

    PubMed

    Todorov, Emanuel

    2009-07-14

    Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress--as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.

  1. On optimal control of linear systems in the presence of multiplicative noise

    NASA Technical Reports Server (NTRS)

    Joshi, S. M.

    1976-01-01

    This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programming. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an 'enforced separation' solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

  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. One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

    NASA Technical Reports Server (NTRS)

    Taasan, Shlomo

    1991-01-01

    The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

  4. 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

  5. Aircraft Trajectories Computation-Prediction-Control. Volume 1 (La Trajectoire de l’Avion Calcul-Prediction-Controle)

    DTIC Science & Technology

    1990-03-01

    knowledge covering problems of this type is called calculus of variations or optimal control theory (Refs. 1-8). As stated before, appli - cations occur...to the optimality conditions and the feasibility equations of Problem (GP), respectively. Clearly, after the transformation (26) is applied , the...trajectories, the primal sequential gradient-restoration algorithm (PSGRA) is applied to compute optimal trajectories for aeroassisted orbital transfer

  6. Analytical design of an industrial two-term controller for optimal regulatory control of open-loop unstable processes under operational constraints.

    PubMed

    Tchamna, Rodrigue; Lee, Moonyong

    2018-01-01

    This paper proposes a novel optimization-based approach for the design of an industrial two-term proportional-integral (PI) controller for the optimal regulatory control of unstable processes subjected to three common operational constraints related to the process variable, manipulated variable and its rate of change. To derive analytical design relations, the constrained optimal control problem in the time domain was transformed into an unconstrained optimization problem in a new parameter space via an effective parameterization. The resulting optimal PI controller has been verified to yield optimal performance and stability of an open-loop unstable first-order process under operational constraints. The proposed analytical design method explicitly takes into account the operational constraints in the controller design stage and also provides useful insights into the optimal controller design. Practical procedures for designing optimal PI parameters and a feasible constraint set exclusive of complex optimization steps are also proposed. The proposed controller was compared with several other PI controllers to illustrate its performance. The robustness of the proposed controller against plant-model mismatch has also been investigated. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  7. Efficient Optimization of Low-Thrust Spacecraft Trajectories

    NASA Technical Reports Server (NTRS)

    Lee, Seungwon; Fink, Wolfgang; Russell, Ryan; Terrile, Richard; Petropoulos, Anastassios; vonAllmen, Paul

    2007-01-01

    A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.

  8. Infinite horizon optimal impulsive control with applications to Internet congestion control

    NASA Astrophysics Data System (ADS)

    Avrachenkov, Konstantin; Habachi, Oussama; Piunovskiy, Alexey; Zhang, Yi

    2015-04-01

    We investigate infinite-horizon deterministic optimal control problems with both gradual and impulsive controls, where any finitely many impulses are allowed simultaneously. Both discounted and long-run time-average criteria are considered. We establish very general and at the same time natural conditions, under which the dynamic programming approach results in an optimal feedback policy. The established theoretical results are applied to the Internet congestion control, and by solving analytically and nontrivially the underlying optimal control problems, we obtain a simple threshold-based active queue management scheme, which takes into account the main parameters of the transmission control protocols, and improves the fairness among the connections in a given network.

  9. A variable-gain output feedback control design methodology

    NASA Technical Reports Server (NTRS)

    Halyo, Nesim; Moerder, Daniel D.; Broussard, John R.; Taylor, Deborah B.

    1989-01-01

    A digital control system design technique is developed in which the control system gain matrix varies with the plant operating point parameters. The design technique is obtained by formulating the problem as an optimal stochastic output feedback control law with variable gains. This approach provides a control theory framework within which the operating range of a control law can be significantly extended. Furthermore, the approach avoids the major shortcomings of the conventional gain-scheduling techniques. The optimal variable gain output feedback control problem is solved by embedding the Multi-Configuration Control (MCC) problem, previously solved at ICS. An algorithm to compute the optimal variable gain output feedback control gain matrices is developed. The algorithm is a modified version of the MCC algorithm improved so as to handle the large dimensionality which arises particularly in variable-gain control problems. The design methodology developed is applied to a reconfigurable aircraft control problem. A variable-gain output feedback control problem was formulated to design a flight control law for an AFTI F-16 aircraft which can automatically reconfigure its control strategy to accommodate failures in the horizontal tail control surface. Simulations of the closed-loop reconfigurable system show that the approach produces a control design which can accommodate such failures with relative ease. The technique can be applied to many other problems including sensor failure accommodation, mode switching control laws and super agility.

  10. Finite horizon optimum control with and without a scrap value

    NASA Astrophysics Data System (ADS)

    Neck, R.; Blueschke-Nikolaeva, V.; Blueschke, D.

    2017-06-01

    In this paper, we study the effects of scrap values on the solutions of optimal control problems with finite time horizon. We show how to include a scrap value, either for the state variables or for the state and the control variables, in the OPTCON2 algorithm for the optimal control of dynamic economic systems. We ask whether the introduction of a scrap value can serve as a substitute for an infinite horizon in economic policy optimization problems where the latter option is not available. Using a simple numerical macroeconomic model, we demonstrate that the introduction of a scrap value cannot induce control policies which can be expected for problems with an infinite time horizon.

  11. The dynamics and optimal control of spinning spacecraft and movable telescoping appendages, part A. [two axis control with single offset boom

    NASA Technical Reports Server (NTRS)

    Bainum, P. M.; Sellappan, R.

    1977-01-01

    The problem of optimal control with a minimum time criterion as applied to a single boom system for achieving two axis control is discussed. The special case where the initial conditions are such that the system can be driven to the equilibrium state with only a single switching maneuver in the bang-bang optimal sequence is analyzed. The system responses are presented. Application of the linear regulator problem for the optimal control of the telescoping system is extended to consider the effects of measurement and plant noises. The noise uncertainties are included with an application of the estimator - Kalman filter problem. Different schemes for measuring the components of the angular velocity are considered. Analytical results are obtained for special cases, and numerical results are presented for the general case.

  12. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  13. Optimality conditions for the numerical solution of optimization problems with PDE constraints :

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

    Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

    2014-03-01

    A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

  14. Algorithm for solving of two-level hierarchical minimax program control problem of final state the regional socio-economic system in the presence of risks

    NASA Astrophysics Data System (ADS)

    Shorikov, A. F.

    2017-10-01

    In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we propose a mathematical model in the form of two-level hierarchical minimax program control problem of the final state of this process with incomplete information. For solving of its problem we constructed the common algorithm that has a form of a recurrent procedure of solving a linear programming and a finite optimization problems.

  15. 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.

  16. 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.

  17. Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

    NASA Astrophysics Data System (ADS)

    Lapin, A.; Romanenko, A.

    2016-11-01

    The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

  18. 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.

  19. Optimal control of LQG problem with an explicit trade-off between mean and variance

    NASA Astrophysics Data System (ADS)

    Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

    2011-12-01

    For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

  20. Guidance and flight control law development for hypersonic vehicles

    NASA Technical Reports Server (NTRS)

    Calise, A. J.; Markopoulos, N.

    1993-01-01

    During the third reporting period our efforts were focused on a reformulation of the optimal control problem involving active state-variable inequality constraints. In the reformulated problem the optimization is carried out not with respect to all controllers, but only with respect to asymptotic controllers leading to the state constraint boundary. Intimately connected with the traditional formulation is the fact that when the reduced solution for such problems lies on a state constraint boundary, the corresponding boundary layer transitions are of finite time in the stretched time scale. Thus, it has been impossible so far to apply the classical asymptotic boundary layer theory to such problems. Moreover, the traditional formulation leads to optimal controllers that are one-sided, that is, they break down when a disturbance throws the system on the prohibited side of the state constraint boundary.

  1. Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

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

    Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef

    2009-10-15

    We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and tomore » the shape optimization problem.« less

  2. Optimal blood glucose control in diabetes mellitus treatment using dynamic programming based on Ackerman’s linear model

    NASA Astrophysics Data System (ADS)

    Pradanti, Paskalia; Hartono

    2018-03-01

    Determination of insulin injection dose in diabetes mellitus treatment can be considered as an optimal control problem. This article is aimed to simulate optimal blood glucose control for patient with diabetes mellitus. The blood glucose regulation of diabetic patient is represented by Ackerman’s Linear Model. This problem is then solved using dynamic programming method. The desired blood glucose level is obtained by minimizing the performance index in Lagrange form. The results show that dynamic programming based on Ackerman’s Linear Model is quite good to solve the problem.

  3. Optimization methods of laws control of electric propulsion spacecraft in the restricted three-body task

    NASA Astrophysics Data System (ADS)

    Starinova, Olga L.

    2014-12-01

    This paper outlines the optimization methods of the control law of the low thrust spacecraft for the restrict problem of three-body. The conditions for fragmentation trajectory on the specific parts of trajectory are formulated. The mathematical statement and methods to solve the optimal control problem on these parts are stated. Results of the decision of applied problems for various classes of spacecrafts which are carrying out maneuvers with low thrust are presented. In particular, the non-coplanar maneuvers of the low thrust spacecraft in the Earth-Moon system are viewed.

  4. A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.

    1991-01-01

    The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.

  5. A multiple objective optimization approach to quality control

    NASA Technical Reports Server (NTRS)

    Seaman, Christopher Michael

    1991-01-01

    The use of product quality as the performance criteria for manufacturing system control is explored. The goal in manufacturing, for economic reasons, is to optimize product quality. The problem is that since quality is a rather nebulous product characteristic, there is seldom an analytic function that can be used as a measure. Therefore standard control approaches, such as optimal control, cannot readily be applied. A second problem with optimizing product quality is that it is typically measured along many dimensions: there are many apsects of quality which must be optimized simultaneously. Very often these different aspects are incommensurate and competing. The concept of optimality must now include accepting tradeoffs among the different quality characteristics. These problems are addressed using multiple objective optimization. It is shown that the quality control problem can be defined as a multiple objective optimization problem. A controller structure is defined using this as the basis. Then, an algorithm is presented which can be used by an operator to interactively find the best operating point. Essentially, the algorithm uses process data to provide the operator with two pieces of information: (1) if it is possible to simultaneously improve all quality criteria, then determine what changes to the process input or controller parameters should be made to do this; and (2) if it is not possible to improve all criteria, and the current operating point is not a desirable one, select a criteria in which a tradeoff should be made, and make input changes to improve all other criteria. The process is not operating at an optimal point in any sense if no tradeoff has to be made to move to a new operating point. This algorithm ensures that operating points are optimal in some sense and provides the operator with information about tradeoffs when seeking the best operating point. The multiobjective algorithm was implemented in two different injection molding scenarios: tuning of process controllers to meet specified performance objectives and tuning of process inputs to meet specified quality objectives. Five case studies are presented.

  6. Real-time control of optimal low-thrust transfer to the Sun-Earth L 1 halo orbit in the bicircular four-body problem

    NASA Astrophysics Data System (ADS)

    Salmani, Majid; Büskens, Christof

    2011-11-01

    In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun-Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L1 is the destination of the mission which is one of the equilibrium points in the Sun-Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.

  7. Application of GA, PSO, and ACO algorithms to path planning of autonomous underwater vehicles

    NASA Astrophysics Data System (ADS)

    Aghababa, Mohammad Pourmahmood; Amrollahi, Mohammad Hossein; Borjkhani, Mehdi

    2012-09-01

    In this paper, an underwater vehicle was modeled with six dimensional nonlinear equations of motion, controlled by DC motors in all degrees of freedom. Near-optimal trajectories in an energetic environment for underwater vehicles were computed using a numerical solution of a nonlinear optimal control problem (NOCP). An energy performance index as a cost function, which should be minimized, was defined. The resulting problem was a two-point boundary value problem (TPBVP). A genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO) algorithms were applied to solve the resulting TPBVP. Applying an Euler-Lagrange equation to the NOCP, a conjugate gradient penalty method was also adopted to solve the TPBVP. The problem of energetic environments, involving some energy sources, was discussed. Some near-optimal paths were found using a GA, PSO, and ACO algorithms. Finally, the problem of collision avoidance in an energetic environment was also taken into account.

  8. Robust control of systems with real parameter uncertainty and unmodelled dynamics

    NASA Technical Reports Server (NTRS)

    Chang, Bor-Chin; Fischl, Robert

    1991-01-01

    During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

  9. Recent experience in simultaneous control-structure optimization

    NASA Technical Reports Server (NTRS)

    Salama, M.; Ramaker, R.; Milman, M.

    1989-01-01

    To show the feasibility of simultaneous optimization as design procedure, low order problems were used in conjunction with simple control formulations. The numerical results indicate that simultaneous optimization is not only feasible, but also advantageous. Such advantages come at the expense of introducing complexities beyond those encountered in structure optimization alone, or control optimization alone. Examples include: larger design parameter space, optimization may combine continuous and combinatoric variables, and the combined objective function may be nonconvex. Future extensions to include large order problems, more complex objective functions and constraints, and more sophisticated control formulations will require further research to ensure that the additional complexities do not outweigh the advantages of simultaneous optimization. Some areas requiring more efficient tools than currently available include: multiobjective criteria and nonconvex optimization. Efficient techniques to deal with optimization over combinatoric and continuous variables, and with truncation issues for structure and control parameters of both the model space as well as the design space need to be developed.

  10. Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

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

    Haslinger, Jaroslav, E-mail: hasling@karlin.mff.cuni.cz; Stebel, Jan, E-mail: stebel@math.cas.cz

    2011-04-15

    We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

  11. 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.

  12. Optimal control in adaptive optics modeling of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Herrmann, J.

    The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

  13. Supercomputer optimizations for stochastic optimal control applications

    NASA Technical Reports Server (NTRS)

    Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

    1991-01-01

    Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

  14. Distributed Optimization

    NASA Technical Reports Server (NTRS)

    Macready, William; Wolpert, David

    2005-01-01

    We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

  15. An approach to optimal semi-active control of vibration energy harvesting based on MEMS

    NASA Astrophysics Data System (ADS)

    Rojas, Rafael A.; Carcaterra, Antonio

    2018-07-01

    In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov's method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.

  16. Optimization of fuel-cell tram operation based on two dimension dynamic programming

    NASA Astrophysics Data System (ADS)

    Zhang, Wenbin; Lu, Xuecheng; Zhao, Jingsong; Li, Jianqiu

    2018-02-01

    This paper proposes an optimal control strategy based on the two-dimension dynamic programming (2DDP) algorithm targeting at minimizing operation energy consumption for a fuel-cell tram. The energy consumption model with the tram dynamics is firstly deduced. Optimal control problem are analyzed and the 2DDP strategy is applied to solve the problem. The optimal tram speed profiles are obtained for each interstation which consist of three stages: accelerate to the set speed with the maximum traction power, dynamically adjust to maintain a uniform speed and decelerate to zero speed with the maximum braking power at a suitable timing. The optimal control curves of all the interstations are connected with the parking time to form the optimal control method of the whole line. The optimized speed profiles are also simplified for drivers to follow.

  17. 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.

  18. 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

  19. UAV path planning using artificial potential field method updated by optimal control theory

    NASA Astrophysics Data System (ADS)

    Chen, Yong-bo; Luo, Guan-chen; Mei, Yue-song; Yu, Jian-qiao; Su, Xiao-long

    2016-04-01

    The unmanned aerial vehicle (UAV) path planning problem is an important assignment in the UAV mission planning. Based on the artificial potential field (APF) UAV path planning method, it is reconstructed into the constrained optimisation problem by introducing an additional control force. The constrained optimisation problem is translated into the unconstrained optimisation problem with the help of slack variables in this paper. The functional optimisation method is applied to reform this problem into an optimal control problem. The whole transformation process is deduced in detail, based on a discrete UAV dynamic model. Then, the path planning problem is solved with the help of the optimal control method. The path following process based on the six degrees of freedom simulation model of the quadrotor helicopters is introduced to verify the practicability of this method. Finally, the simulation results show that the improved method is more effective in planning path. In the planning space, the length of the calculated path is shorter and smoother than that using traditional APF method. In addition, the improved method can solve the dead point problem effectively.

  20. Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

    NASA Astrophysics Data System (ADS)

    Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

    2018-04-01

    This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

  1. Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

    NASA Technical Reports Server (NTRS)

    Acikmese, Behcet A.; Carson, John M., III

    2005-01-01

    A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

  2. A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Carson, John M., III

    2006-01-01

    A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

  3. Robust fuel- and time-optimal control of uncertain flexible space structures

    NASA Technical Reports Server (NTRS)

    Wie, Bong; Sinha, Ravi; Sunkel, John; Cox, Ken

    1993-01-01

    The problem of computing open-loop, fuel- and time-optimal control inputs for flexible space structures in the face of modeling uncertainty is investigated. Robustified, fuel- and time-optimal pulse sequences are obtained by solving a constrained optimization problem subject to robustness constraints. It is shown that 'bang-off-bang' pulse sequences with a finite number of switchings provide a practical tradeoff among the maneuvering time, fuel consumption, and performance robustness of uncertain flexible space structures.

  4. Physical insight into the simultaneous optimization of structure and control

    NASA Technical Reports Server (NTRS)

    Jacques, Robert N.; Miller, David W.

    1993-01-01

    Recent trends in spacecraft design which yield larger structures with more stringent performance requirements place many flexible modes of the structure within the bandwidth of active controllers. The resulting complications to the spacecraft design make it highly desirable to understand the impact of structural changes on an optimally controlled structure. This work uses low structural models with optimal H(sub 2) and H(sub infinity) controllers to develop some basic insight into this problem. This insight concentrates on several basic approaches to improving controlled performance and how these approaches interact in determining the optimal designs. A numerical example is presented to demonstrate how this insight can be generalized to more complex problems.

  5. Randomly Sampled-Data Control Systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Han, Kuoruey

    1990-01-01

    The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

  6. Optimal and Autonomous Control Using Reinforcement Learning: A Survey.

    PubMed

    Kiumarsi, Bahare; Vamvoudakis, Kyriakos G; Modares, Hamidreza; Lewis, Frank L

    2018-06-01

    This paper reviews the current state of the art on reinforcement learning (RL)-based feedback control solutions to optimal regulation and tracking of single and multiagent systems. Existing RL solutions to both optimal and control problems, as well as graphical games, will be reviewed. RL methods learn the solution to optimal control and game problems online and using measured data along the system trajectories. We discuss Q-learning and the integral RL algorithm as core algorithms for discrete-time (DT) and continuous-time (CT) systems, respectively. Moreover, we discuss a new direction of off-policy RL for both CT and DT systems. Finally, we review several applications.

  7. On the decentralized control of large-scale systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Chong, C.

    1973-01-01

    The decentralized control of stochastic large scale systems was considered. Particular emphasis was given to control strategies which utilize decentralized information and can be computed in a decentralized manner. The deterministic constrained optimization problem is generalized to the stochastic case when each decision variable depends on different information and the constraint is only required to be satisfied on the average. For problems with a particular structure, a hierarchical decomposition is obtained. For the stochastic control of dynamic systems with different information sets, a new kind of optimality is proposed which exploits the coupled nature of the dynamic system. The subsystems are assumed to be uncoupled and then certain constraints are required to be satisfied, either in a off-line or on-line fashion. For off-line coordination, a hierarchical approach of solving the problem is obtained. The lower level problems are all uncoupled. For on-line coordination, distinction is made between open loop feedback optimal coordination and closed loop optimal coordination.

  8. Minimal complexity control law synthesis

    NASA Technical Reports Server (NTRS)

    Bernstein, Dennis S.; Haddad, Wassim M.; Nett, Carl N.

    1989-01-01

    A paradigm for control law design for modern engineering systems is proposed: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. Correspondingly, the overall goal is to make progress towards the development of a control law design methodology which supports this paradigm. Researchers achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation, where here constrained-structure means that the dynamic-structure (e.g., dynamic order, pole locations, zero locations, etc.) of the output feedback compensation is constrained in some way. By applying this theory in an innovative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can, in principle, be realized. The optimal constrained-structure dynamic output feedback problem is formulated in general terms. An elegant method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is then developed. This reduction procedure makes use of star products, linear fractional transformations, and linear fractional decompositions, and yields as a byproduct a complete characterization of the class of optimal constrained-structure dynamic output feedback problems which can be reduced to optimal static output feedback problems. Issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations are considered, and it is shown how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by constraining the controller dynamic-structure in an appropriate fashion.

  9. Feedback control for fuel-optimal descents using singular perturbation techniques

    NASA Technical Reports Server (NTRS)

    Price, D. B.

    1984-01-01

    In response to rising fuel costs and reduced profit margins for the airline companies, the optimization of the paths flown by transport aircraft has been considered. It was found that application of optimal control theory to the considered problem can result in savings in fuel, time, and direct operating costs. The best solution to the aircraft trajectory problem is an onboard real-time feedback control law. The present paper presents a technique which shows promise of becoming a part of a complete solution. The application of singular perturbation techniques to the problem is discussed, taking into account the benefits and some problems associated with them. A different technique for handling the descent part of a trajectory is also discussed.

  10. Application of controller partitioning optimization procedure to integrated flight/propulsion control design for a STOVL aircraft

    NASA Technical Reports Server (NTRS)

    Garg, Sanjay; Schmidt, Phillip H.

    1993-01-01

    A parameter optimization framework has earlier been developed to solve the problem of partitioning a centralized controller into a decentralized, hierarchical structure suitable for integrated flight/propulsion control implementation. This paper presents results from the application of the controller partitioning optimization procedure to IFPC design for a Short Take-Off and Vertical Landing (STOVL) aircraft in transition flight. The controller partitioning problem and the parameter optimization algorithm are briefly described. Insight is provided into choosing various 'user' selected parameters in the optimization cost function such that the resulting optimized subcontrollers will meet the characteristics of the centralized controller that are crucial to achieving the desired closed-loop performance and robustness, while maintaining the desired subcontroller structure constraints that are crucial for IFPC implementation. The optimization procedure is shown to improve upon the initial partitioned subcontrollers and lead to performance comparable to that achieved with the centralized controller. This application also provides insight into the issues that should be addressed at the centralized control design level in order to obtain implementable partitioned subcontrollers.

  11. Analogue of the Kelley condition for optimal systems with retarded control

    NASA Astrophysics Data System (ADS)

    Mardanov, Misir J.; Melikov, Telman K.

    2017-07-01

    In this paper, we consider an optimal control problem with retarded control and study a larger class of singular (in the classical sense) controls. The Kelley and equality type optimality conditions are obtained. To prove our main results, we use the Legendre polynomials as variations of control.

  12. Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

    NASA Astrophysics Data System (ADS)

    Alekseev, G.; Tokhtina, A.; Soboleva, O.

    2017-10-01

    Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

  13. Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

    NASA Technical Reports Server (NTRS)

    Balling, R. J.; Wilkinson, C. A.

    1997-01-01

    A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

  14. Dynamic optimization case studies in DYNOPT tool

    NASA Astrophysics Data System (ADS)

    Ozana, Stepan; Pies, Martin; Docekal, Tomas

    2016-06-01

    Dynamic programming is typically applied to optimization problems. As the analytical solutions are generally very difficult, chosen software tools are used widely. These software packages are often third-party products bound for standard simulation software tools on the market. As typical examples of such tools, TOMLAB and DYNOPT could be effectively applied for solution of problems of dynamic programming. DYNOPT will be presented in this paper due to its licensing policy (free product under GPL) and simplicity of use. DYNOPT is a set of MATLAB functions for determination of optimal control trajectory by given description of the process, the cost to be minimized, subject to equality and inequality constraints, using orthogonal collocation on finite elements method. The actual optimal control problem is solved by complete parameterization both the control and the state profile vector. It is assumed, that the optimized dynamic model may be described by a set of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs). This collection of functions extends the capability of the MATLAB Optimization Tool-box. The paper will introduce use of DYNOPT in the field of dynamic optimization problems by means of case studies regarding chosen laboratory physical educational models.

  15. Epidemic spreading on random surfer networks with optimal interaction radius

    NASA Astrophysics Data System (ADS)

    Feng, Yun; Ding, Li; Hu, Ping

    2018-03-01

    In this paper, the optimal control problem of epidemic spreading on random surfer heterogeneous networks is considered. An epidemic spreading model is established according to the classification of individual's initial interaction radii. Then, a control strategy is proposed based on adjusting individual's interaction radii. The global stability of the disease free and endemic equilibrium of the model is investigated. We prove that an optimal solution exists for the optimal control problem and the explicit form of which is presented. Numerical simulations are conducted to verify the correctness of the theoretical results. It is proved that the optimal control strategy is effective to minimize the density of infected individuals and the cost associated with the adjustment of interaction radii.

  16. Design of optimally normal minimum gain controllers by continuation method

    NASA Technical Reports Server (NTRS)

    Lim, K. B.; Juang, J.-N.; Kim, Z. C.

    1989-01-01

    A measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First- and second-order necessary conditions for the constrained optimization problem are derived and solved by a Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.

  17. Optimal control of nonlinear continuous-time systems in strict-feedback form.

    PubMed

    Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani

    2015-10-01

    This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.

  18. 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

  19. Optimal Strategy for Integrated Dynamic Inventory Control and Supplier Selection in Unknown Environment via Stochastic Dynamic Programming

    NASA Astrophysics Data System (ADS)

    Sutrisno; Widowati; Solikhin

    2016-06-01

    In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.

  20. Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

    NASA Astrophysics Data System (ADS)

    Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

    2017-01-01

    This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

  1. A neural network based implementation of an MPC algorithm applied in the control systems of electromechanical plants

    NASA Astrophysics Data System (ADS)

    Marusak, Piotr M.; Kuntanapreeda, Suwat

    2018-01-01

    The paper considers application of a neural network based implementation of a model predictive control (MPC) control algorithm to electromechanical plants. Properties of such control plants implicate that a relatively short sampling time should be used. However, in such a case, finding the control value numerically may be too time-consuming. Therefore, the current paper tests the solution based on transforming the MPC optimization problem into a set of differential equations whose solution is the same as that of the original optimization problem. This set of differential equations can be interpreted as a dynamic neural network. In such an approach, the constraints can be introduced into the optimization problem with relative ease. Moreover, the solution of the optimization problem can be obtained faster than when the standard numerical quadratic programming routine is used. However, a very careful tuning of the algorithm is needed to achieve this. A DC motor and an electrohydraulic actuator are taken as illustrative examples. The feasibility and effectiveness of the proposed approach are demonstrated through numerical simulations.

  2. Optimality of affine control system of several species in competition on a sequential batch reactor

    NASA Astrophysics Data System (ADS)

    Rodríguez, J. C.; Ramírez, H.; Gajardo, P.; Rapaport, A.

    2014-09-01

    In this paper, we analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which we apply different optimality conditions derived from Pontryagin principle and the Hamilton-Jacobi-Bellman equation. We thus characterise the singular trajectories of our problem as the extremal trajectories keeping the substrate at a constant level. We also establish conditions for which an immediate one impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy.

  3. Interdisciplinary optimum design. [of aerospace structures

    NASA Technical Reports Server (NTRS)

    Sobieszczanski-Sobieski, Jaroslaw; Haftka, Raphael T.

    1986-01-01

    Problems related to interdisciplinary interactions in the design of a complex engineering systems are examined with reference to aerospace applications. The interdisciplinary optimization problems examined include those dealing with controls and structures, materials and structures, control and stability, structure and aerodynamics, and structure and thermodynamics. The discussion is illustrated by the following specific applications: integrated aerodynamic/structural optimization of glider wing; optimization of an antenna parabolic dish structure for minimum weight and prescribed emitted signal gain; and a multilevel optimization study of a transport aircraft.

  4. 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.

  5. Optimal Control Inventory Stochastic With Production Deteriorating

    NASA Astrophysics Data System (ADS)

    Affandi, Pardi

    2018-01-01

    In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

  6. Non-adaptive and adaptive hybrid approaches for enhancing water quality management

    NASA Astrophysics Data System (ADS)

    Kalwij, Ineke M.; Peralta, Richard C.

    2008-09-01

    SummaryUsing optimization to help solve groundwater management problems cost-effectively is becoming increasingly important. Hybrid optimization approaches, that combine two or more optimization algorithms, will become valuable and common tools for addressing complex nonlinear hydrologic problems. Hybrid heuristic optimizers have capabilities far beyond those of a simple genetic algorithm (SGA), and are continuously improving. SGAs having only parent selection, crossover, and mutation are inefficient and rarely used for optimizing contaminant transport management. Even an advanced genetic algorithm (AGA) that includes elitism (to emphasize using the best strategies as parents) and healing (to help assure optimal strategy feasibility) is undesirably inefficient. Much more efficient than an AGA is the presented hybrid (AGCT), which adds comprehensive tabu search (TS) features to an AGA. TS mechanisms (TS probability, tabu list size, search coarseness and solution space size, and a TS threshold value) force the optimizer to search portions of the solution space that yield superior pumping strategies, and to avoid reproducing similar or inferior strategies. An AGCT characteristic is that TS control parameters are unchanging during optimization. However, TS parameter values that are ideal for optimization commencement can be undesirable when nearing assumed global optimality. The second presented hybrid, termed global converger (GC), is significantly better than the AGCT. GC includes AGCT plus feedback-driven auto-adaptive control that dynamically changes TS parameters during run-time. Before comparing AGCT and GC, we empirically derived scaled dimensionless TS control parameter guidelines by evaluating 50 sets of parameter values for a hypothetical optimization problem. For the hypothetical area, AGCT optimized both well locations and pumping rates. The parameters are useful starting values because using trial-and-error to identify an ideal combination of control parameter values for a new optimization problem can be time consuming. For comparison, AGA, AGCT, and GC are applied to optimize pumping rates for assumed well locations of a complex large-scale contaminant transport and remediation optimization problem at Blaine Naval Ammunition Depot (NAD). Both hybrid approaches converged more closely to the optimal solution than the non-hybrid AGA. GC averaged 18.79% better convergence than AGCT, and 31.9% than AGA, within the same computation time (12.5 days). AGCT averaged 13.1% better convergence than AGA. The GC can significantly reduce the burden of employing computationally intensive hydrologic simulation models within a limited time period and for real-world optimization problems. Although demonstrated for a groundwater quality problem, it is also applicable to other arenas, such as managing salt water intrusion and surface water contaminant loading.

  7. A Framework for Optimal Control Allocation with Structural Load Constraints

    NASA Technical Reports Server (NTRS)

    Frost, Susan A.; Taylor, Brian R.; Jutte, Christine V.; Burken, John J.; Trinh, Khanh V.; Bodson, Marc

    2010-01-01

    Conventional aircraft generally employ mixing algorithms or lookup tables to determine control surface deflections needed to achieve moments commanded by the flight control system. Control allocation is the problem of converting desired moments into control effector commands. Next generation aircraft may have many multipurpose, redundant control surfaces, adding considerable complexity to the control allocation problem. These issues can be addressed with optimal control allocation. Most optimal control allocation algorithms have control surface position and rate constraints. However, these constraints are insufficient to ensure that the aircraft's structural load limits will not be exceeded by commanded surface deflections. In this paper, a framework is proposed to enable a flight control system with optimal control allocation to incorporate real-time structural load feedback and structural load constraints. A proof of concept simulation that demonstrates the framework in a simulation of a generic transport aircraft is presented.

  8. Trajectory optimization for the National Aerospace Plane

    NASA Technical Reports Server (NTRS)

    Lu, Ping

    1992-01-01

    The primary objective of this research is to develop an efficient and robust trajectory optimization tool for the optimal ascent problem of the National Aerospace Plane (NASP). This report is organized in the following order to summarize the complete work: Section two states the formulation and models of the trajectory optimization problem. An inverse dynamics approach to the problem is introduced in Section three. Optimal trajectories corresponding to various conditions and performance parameters are presented in Section four. A midcourse nonlinear feedback controller is developed in Section five. Section six demonstrates the performance of the inverse dynamics approach and midcourse controller during disturbances. Section seven discusses rocket assisted ascent which may be beneficial when orbital altitude is high. Finally, Section eight recommends areas of future research.

  9. Environmental optimal control strategies based on plant canopy photosynthesis responses and greenhouse climate model

    NASA Astrophysics Data System (ADS)

    Deng, Lujuan; Xie, Songhe; Cui, Jiantao; Liu, Tao

    2006-11-01

    It is the essential goal of intelligent greenhouse environment optimal control to enhance income of cropper and energy save. There were some characteristics such as uncertainty, imprecision, nonlinear, strong coupling, bigger inertia and different time scale in greenhouse environment control system. So greenhouse environment optimal control was not easy and especially model-based optimal control method was more difficult. So the optimal control problem of plant environment in intelligent greenhouse was researched. Hierarchical greenhouse environment control system was constructed. In the first level data measuring was carried out and executive machine was controlled. Optimal setting points of climate controlled variable in greenhouse was calculated and chosen in the second level. Market analysis and planning were completed in third level. The problem of the optimal setting point was discussed in this paper. Firstly the model of plant canopy photosynthesis responses and the model of greenhouse climate model were constructed. Afterwards according to experience of the planting expert, in daytime the optimal goals were decided according to the most maximal photosynthesis rate principle. In nighttime on plant better growth conditions the optimal goals were decided by energy saving principle. Whereafter environment optimal control setting points were computed by GA. Compared the optimal result and recording data in real system, the method is reasonable and can achieve energy saving and the maximal photosynthesis rate in intelligent greenhouse

  10. Results of an integrated structure-control law design sensitivity analysis

    NASA Technical Reports Server (NTRS)

    Gilbert, Michael G.

    1988-01-01

    Next generation air and space vehicle designs are driven by increased performance requirements, demanding a high level of design integration between traditionally separate design disciplines. Interdisciplinary analysis capabilities have been developed, for aeroservoelastic aircraft and large flexible spacecraft control for instance, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changess in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient that finite difference methods for the computation of the equivalent sensitivity information.

  11. Near-optimal, asymptotic tracking in control problems involving state-variable inequality constraints

    NASA Technical Reports Server (NTRS)

    Markopoulos, N.; Calise, A. J.

    1993-01-01

    The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.

  12. Performance Optimizing Multi-Objective Adaptive Control with Time-Varying Model Reference Modification

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Hashemi, Kelley E.; Yucelen, Tansel; Arabi, Ehsan

    2017-01-01

    This paper presents a new adaptive control approach that involves a performance optimization objective. The problem is cast as a multi-objective optimal control. The control synthesis involves the design of a performance optimizing controller from a subset of control inputs. The effect of the performance optimizing controller is to introduce an uncertainty into the system that can degrade tracking of the reference model. An adaptive controller from the remaining control inputs is designed to reduce the effect of the uncertainty while maintaining a notion of performance optimization in the adaptive control system.

  13. A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

    NASA Astrophysics Data System (ADS)

    Sandhu, Amit

    A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

  14. Optimal control design of turbo spin‐echo sequences with applications to parallel‐transmit systems

    PubMed Central

    Hoogduin, Hans; Hajnal, Joseph V.; van den Berg, Cornelis A. T.; Luijten, Peter R.; Malik, Shaihan J.

    2016-01-01

    Purpose The design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online. Theory and Methods The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations. Results Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields. Conclusion The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine PMID:26800383

  15. Multi Objective Controller Design for Linear System via Optimal Interpolation

    NASA Technical Reports Server (NTRS)

    Ozbay, Hitay

    1996-01-01

    We propose a methodology for the design of a controller which satisfies a set of closed-loop objectives simultaneously. The set of objectives consists of: (1) pole placement, (2) decoupled command tracking of step inputs at steady-state, and (3) minimization of step response transients with respect to envelope specifications. We first obtain a characterization of all controllers placing the closed-loop poles in a prescribed region of the complex plane. In this characterization, the free parameter matrix Q(s) is to be determined to attain objectives (2) and (3). Objective (2) is expressed as determining a Pareto optimal solution to a vector valued optimization problem. The solution of this problem is obtained by transforming it to a scalar convex optimization problem. This solution determines Q(O) and the remaining freedom in choosing Q(s) is used to satisfy objective (3). We write Q(s) = (l/v(s))bar-Q(s) for a prescribed polynomial v(s). Bar-Q(s) is a polynomial matrix which is arbitrary except that Q(O) and the order of bar-Q(s) are fixed. Obeying these constraints bar-Q(s) is now to be 'shaped' to minimize the step response characteristics of specific input/output pairs according to the maximum envelope violations. This problem is expressed as a vector valued optimization problem using the concept of Pareto optimality. We then investigate a scalar optimization problem associated with this vector valued problem and show that it is convex. The organization of the report is as follows. The next section includes some definitions and preliminary lemmas. We then give the problem statement which is followed by a section including a detailed development of the design procedure. We then consider an aircraft control example. The last section gives some concluding remarks. The Appendix includes the proofs of technical lemmas, printouts of computer programs, and figures.

  16. Distributed Optimization of Multi-Agent Systems: Framework, Local Optimizer, and Applications

    NASA Astrophysics Data System (ADS)

    Zu, Yue

    Convex optimization problem can be solved in a centralized or distributed manner. Compared with centralized methods based on single-agent system, distributed algorithms rely on multi-agent systems with information exchanging among connected neighbors, which leads to great improvement on the system fault tolerance. Thus, a task within multi-agent system can be completed with presence of partial agent failures. By problem decomposition, a large-scale problem can be divided into a set of small-scale sub-problems that can be solved in sequence/parallel. Hence, the computational complexity is greatly reduced by distributed algorithm in multi-agent system. Moreover, distributed algorithm allows data collected and stored in a distributed fashion, which successfully overcomes the drawbacks of using multicast due to the bandwidth limitation. Distributed algorithm has been applied in solving a variety of real-world problems. Our research focuses on the framework and local optimizer design in practical engineering applications. In the first one, we propose a multi-sensor and multi-agent scheme for spatial motion estimation of a rigid body. Estimation performance is improved in terms of accuracy and convergence speed. Second, we develop a cyber-physical system and implement distributed computation devices to optimize the in-building evacuation path when hazard occurs. The proposed Bellman-Ford Dual-Subgradient path planning method relieves the congestion in corridor and the exit areas. At last, highway traffic flow is managed by adjusting speed limits to minimize the fuel consumption and travel time in the third project. Optimal control strategy is designed through both centralized and distributed algorithm based on convex problem formulation. Moreover, a hybrid control scheme is presented for highway network travel time minimization. Compared with no controlled case or conventional highway traffic control strategy, the proposed hybrid control strategy greatly reduces total travel time on test highway network.

  17. 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.

  18. 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).

  19. Fuel optimization for low-thrust Earth-Moon transfer via indirect optimal control

    NASA Astrophysics Data System (ADS)

    Pérez-Palau, Daniel; Epenoy, Richard

    2018-02-01

    The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun-Earth-Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin's Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem's state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth-Moon and Sun-Earth is presented leading to a physical interpretation of the different families of trajectories.

  20. Computational experiments in the optimal slewing of flexible structures

    NASA Technical Reports Server (NTRS)

    Baker, T. E.; Polak, Lucian Elijah

    1989-01-01

    Numerical experiments on the problem of moving a flexible beam are discussed. An optimal control problem is formulated and transcribed into a form which can be solved using semi-infinite optimization techniques. All experiments were carried out on a SUN 3 microcomputer.

  1. Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

    NASA Technical Reports Server (NTRS)

    Pinson, Robin M.; Lu, Ping

    2016-01-01

    Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

  2. Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.

    PubMed

    Zhang, Qichao; Zhao, Dongbin; Wang, Ding

    2018-01-01

    In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.

  3. 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.

  4. A duality framework for stochastic optimal control of complex systems

    DOE PAGES

    Malikopoulos, Andreas A.

    2016-01-01

    In this study, we address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations having constraints consistent with those studied here, our results imply that the Pareto control policy may be of value when we seek to derivemore » online the optimal control policy in complex systems.« less

  5. Multidisciplinary optimization of a controlled space structure using 150 design variables

    NASA Technical Reports Server (NTRS)

    James, Benjamin B.

    1993-01-01

    A controls-structures interaction design method is presented. The method coordinates standard finite-element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structure and control system of a spacecraft. Global sensitivity equations are used to account for coupling between the disciplines. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Design problems using 15, 63, and 150 design variables to optimize truss member sizes and feedback gain values are solved and the results are presented. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporation of the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables.

  6. Algorithms for Maneuvering Spacecraft Around Small Bodies

    NASA Technical Reports Server (NTRS)

    Acikmese, A. Bechet; Bayard, David

    2006-01-01

    A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

  7. Discrete optimal control approach to a four-dimensional guidance problem near terminal areas

    NASA Technical Reports Server (NTRS)

    Nagarajan, N.

    1974-01-01

    Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.

  8. A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

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

    Addona, Davide, E-mail: d.addona@campus.unimib.it

    2015-08-15

    We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

  9. 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.

  10. 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.

  11. Optimal trajectories of aircraft and spacecraft

    NASA Technical Reports Server (NTRS)

    Miele, A.

    1990-01-01

    Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful engineering compromise between energy requirements and aerodynamics heating requirements.

  12. Optimal Control of Induction Machines to Minimize Transient Energy Losses

    NASA Astrophysics Data System (ADS)

    Plathottam, Siby Jose

    Induction machines are electromechanical energy conversion devices comprised of a stator and a rotor. Torque is generated due to the interaction between the rotating magnetic field from the stator, and the current induced in the rotor conductors. Their speed and torque output can be precisely controlled by manipulating the magnitude, frequency, and phase of the three input sinusoidal voltage waveforms. Their ruggedness, low cost, and high efficiency have made them ubiquitous component of nearly every industrial application. Thus, even a small improvement in their energy efficient tend to give a large amount of electrical energy savings over the lifetime of the machine. Hence, increasing energy efficiency (reducing energy losses) in induction machines is a constrained optimization problem that has attracted attention from researchers. The energy conversion efficiency of induction machines depends on both the speed-torque operating point, as well as the input voltage waveform. It also depends on whether the machine is in the transient or steady state. Maximizing energy efficiency during steady state is a Static Optimization problem, that has been extensively studied, with commercial solutions available. On the other hand, improving energy efficiency during transients is a Dynamic Optimization problem that is sparsely studied. This dissertation exclusively focuses on improving energy efficiency during transients. This dissertation treats the transient energy loss minimization problem as an optimal control problem which consists of a dynamic model of the machine, and a cost functional. The rotor field oriented current fed model of the induction machine is selected as the dynamic model. The rotor speed and rotor d-axis flux are the state variables in the dynamic model. The stator currents referred to as d-and q-axis currents are the control inputs. A cost functional is proposed that assigns a cost to both the energy losses in the induction machine, as well as the deviations from desired speed-torque-magnetic flux setpoints. Using Pontryagin's minimum principle, a set of necessary conditions that must be satisfied by the optimal control trajectories are derived. The conditions are in the form a two-point boundary value problem, that can be solved numerically. The conjugate gradient method that was modified using the Hestenes-Stiefel formula was used to obtain the numerical solution of both the control and state trajectories. Using the distinctive shape of the numerical trajectories as inspiration, analytical expressions were derived for the state, and control trajectories. It was shown that the trajectory could be fully described by finding the solution of a one-dimensional optimization problem. The sensitivity of both the optimal trajectory and the optimal energy efficiency to different induction machine parameters were analyzed. A non-iterative solution that can use feedback for generating optimal control trajectories in real time was explored. It was found that an artificial neural network could be trained using the numerical solutions and made to emulate the optimal control trajectories with a high degree of accuracy. Hence a neural network along with a supervisory logic was implemented and used in a real-time simulation to control the Finite Element Method model of the induction machine. The results were compared with three other control regimes and the optimal control system was found to have the highest energy efficiency for the same drive cycle.

  13. Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

    NASA Astrophysics Data System (ADS)

    Sutrisno; Widowati; Sunarsih; Kartono

    2018-01-01

    In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

  14. Minimal Time Problem with Impulsive Controls

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

    Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at; Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at

    Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.

  15. Robust on-off pulse control of flexible space vehicles

    NASA Technical Reports Server (NTRS)

    Wie, Bong; Sinha, Ravi

    1993-01-01

    The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated.

  16. A variable-gain output feedback control design approach

    NASA Technical Reports Server (NTRS)

    Haylo, Nesim

    1989-01-01

    A multi-model design technique to find a variable-gain control law defined over the whole operating range is proposed. The design is formulated as an optimal control problem which minimizes a cost function weighing the performance at many operating points. The solution is obtained by embedding into the Multi-Configuration Control (MCC) problem, a multi-model robust control design technique. In contrast to conventional gain scheduling which uses a curve fit of single model designs, the optimal variable-gain control law stabilizes the plant at every operating point included in the design. An iterative algorithm to compute the optimal control gains is presented. The methodology has been successfully applied to reconfigurable aircraft flight control and to nonlinear flight control systems.

  17. The individual time trial as an optimal control problem

    PubMed Central

    de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, AL

    2017-01-01

    In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial. PMID:29388631

  18. Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

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

    Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

    We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

  19. Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

    PubMed

    Fan, Quan-Yong; Yang, Guang-Hong

    2017-01-01

    The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  20. Separation-Compliant, Optimal Routing and Control of Scheduled Arrivals in a Terminal Airspace

    NASA Technical Reports Server (NTRS)

    Sadovsky, Alexander V.; Davis, Damek; Isaacson, Douglas R.

    2013-01-01

    We address the problem of navigating a set (fleet) of aircraft in an aerial route network so as to bring each aircraft to its destination at a specified time and with minimal distance separation assured between all aircraft at all times. The speed range, initial position, required destination, and required time of arrival at destination for each aircraft are assumed provided. Each aircraft's movement is governed by a controlled differential equation (state equation). The problem consists in choosing for each aircraft a path in the route network and a control strategy so as to meet the constraints and reach the destination at the required time. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver. The proposed model is first step toward increasing the fidelity of continuous time control models of air traffic in a terminal airspace. The Pontryagin Maximum Principle implies the polygonal shape of those portions of the state trajectories away from those states in which one or more aircraft pair are at minimal separation. The model also confirms the intuition that, the narrower the allowed speed ranges of the aircraft, the smaller the space of optimal solutions, and that an instance of the optimal control problem may not have a solution at all (i.e., no control strategy that meets the separation requirement and other constraints).

  1. On the theory of singular optimal controls in dynamic systems with control delay

    NASA Astrophysics Data System (ADS)

    Mardanov, M. J.; Melikov, T. K.

    2017-05-01

    An optimal control problem with a control delay is considered, and a more broad class of singular (in classical sense) controls is investigated. Various sequences of necessary conditions for the optimality of singular controls in recurrent form are obtained. These optimality conditions include analogues of the Kelley, Kopp-Moyer, R. Gabasov, and equality-type conditions. In the proof of the main results, the variation of the control is defined using Legendre polynomials.

  2. Results of an integrated structure/control law design sensitivity analysis

    NASA Technical Reports Server (NTRS)

    Gilbert, Michael G.

    1989-01-01

    A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information.

  3. Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

    NASA Astrophysics Data System (ADS)

    Li, J. C.; Gong, B.; Wang, H. G.

    2016-08-01

    Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design-determining well placement, number of fracturing stages, and fracture lengths-is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.

  4. Multiresolution strategies for the numerical solution of optimal control problems

    NASA Astrophysics Data System (ADS)

    Jain, Sachin

    There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

  5. Optimal design and control of an electromechanical transfemoral prosthesis with energy regeneration.

    PubMed

    Rohani, Farbod; Richter, Hanz; van den Bogert, Antonie J

    2017-01-01

    In this paper, we present the design of an electromechanical above-knee active prosthesis with energy storage and regeneration. The system consists of geared knee and ankle motors, parallel springs for each motor, an ultracapacitor, and controllable four-quadrant power converters. The goal is to maximize the performance of the system by finding optimal controls and design parameters. A model of the system dynamics was developed, and used to solve a combined trajectory and design optimization problem. The objectives of the optimization were to minimize tracking error relative to human joint motions, as well as energy use. The optimization problem was solved by the method of direct collocation, based on joint torque and joint angle data from ten subjects walking at three speeds. After optimization of controls and design parameters, the simulated system could operate at zero energy cost while still closely emulating able-bodied gait. This was achieved by controlled energy transfer between knee and ankle, and by controlled storage and release of energy throughout the gait cycle. Optimal gear ratios and spring parameters were similar across subjects and walking speeds.

  6. A parameter optimization approach to controller partitioning for integrated flight/propulsion control application

    NASA Technical Reports Server (NTRS)

    Schmidt, Phillip; Garg, Sanjay; Holowecky, Brian

    1992-01-01

    A parameter optimization framework is presented to solve the problem of partitioning a centralized controller into a decentralized hierarchical structure suitable for integrated flight/propulsion control implementation. The controller partitioning problem is briefly discussed and a cost function to be minimized is formulated, such that the resulting 'optimal' partitioned subsystem controllers will closely match the performance (including robustness) properties of the closed-loop system with the centralized controller while maintaining the desired controller partitioning structure. The cost function is written in terms of parameters in a state-space representation of the partitioned sub-controllers. Analytical expressions are obtained for the gradient of this cost function with respect to parameters, and an optimization algorithm is developed using modern computer-aided control design and analysis software. The capabilities of the algorithm are demonstrated by application to partitioned integrated flight/propulsion control design for a modern fighter aircraft in the short approach to landing task. The partitioning optimization is shown to lead to reduced-order subcontrollers that match the closed-loop command tracking and decoupling performance achieved by a high-order centralized controller.

  7. A parameter optimization approach to controller partitioning for integrated flight/propulsion control application

    NASA Technical Reports Server (NTRS)

    Schmidt, Phillip H.; Garg, Sanjay; Holowecky, Brian R.

    1993-01-01

    A parameter optimization framework is presented to solve the problem of partitioning a centralized controller into a decentralized hierarchical structure suitable for integrated flight/propulsion control implementation. The controller partitioning problem is briefly discussed and a cost function to be minimized is formulated, such that the resulting 'optimal' partitioned subsystem controllers will closely match the performance (including robustness) properties of the closed-loop system with the centralized controller while maintaining the desired controller partitioning structure. The cost function is written in terms of parameters in a state-space representation of the partitioned sub-controllers. Analytical expressions are obtained for the gradient of this cost function with respect to parameters, and an optimization algorithm is developed using modern computer-aided control design and analysis software. The capabilities of the algorithm are demonstrated by application to partitioned integrated flight/propulsion control design for a modern fighter aircraft in the short approach to landing task. The partitioning optimization is shown to lead to reduced-order subcontrollers that match the closed-loop command tracking and decoupling performance achieved by a high-order centralized controller.

  8. Analysis of a Two-Dimensional Thermal Cloaking Problem on the Basis of Optimization

    NASA Astrophysics Data System (ADS)

    Alekseev, G. V.

    2018-04-01

    For a two-dimensional model of thermal scattering, inverse problems arising in the development of tools for cloaking material bodies on the basis of a mixed thermal cloaking strategy are considered. By applying the optimization approach, these problems are reduced to optimization ones in which the role of controls is played by variable parameters of the medium occupying the cloaking shell and by the heat flux through a boundary segment of the basic domain. The solvability of the direct and optimization problems is proved, and an optimality system is derived. Based on its analysis, sufficient conditions on the input data are established that ensure the uniqueness and stability of optimal solutions.

  9. Discrete-time Markovian-jump linear quadratic optimal control

    NASA Technical Reports Server (NTRS)

    Chizeck, H. J.; Willsky, A. S.; Castanon, D.

    1986-01-01

    This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

  10. Artificial Intelligence Based Control Power Optimization on Tailless Aircraft. [ARMD Seedling Fund Phase I

    NASA Technical Reports Server (NTRS)

    Gern, Frank; Vicroy, Dan D.; Mulani, Sameer B.; Chhabra, Rupanshi; Kapania, Rakesh K.; Schetz, Joseph A.; Brown, Derrell; Princen, Norman H.

    2014-01-01

    Traditional methods of control allocation optimization have shown difficulties in exploiting the full potential of controlling large arrays of control devices on innovative air vehicles. Artificial neutral networks are inspired by biological nervous systems and neurocomputing has successfully been applied to a variety of complex optimization problems. This project investigates the potential of applying neurocomputing to the control allocation optimization problem of Hybrid Wing Body (HWB) aircraft concepts to minimize control power, hinge moments, and actuator forces, while keeping system weights within acceptable limits. The main objective of this project is to develop a proof-of-concept process suitable to demonstrate the potential of using neurocomputing for optimizing actuation power for aircraft featuring multiple independently actuated control surfaces. A Nastran aeroservoelastic finite element model is used to generate a learning database of hinge moment and actuation power characteristics for an array of flight conditions and control surface deflections. An artificial neural network incorporating a genetic algorithm then uses this training data to perform control allocation optimization for the investigated aircraft configuration. The phase I project showed that optimization results for the sum of required hinge moments are improved by more than 12% over the best Nastran solution by using the neural network optimization process.

  11. Mixed H(2)/H(sub infinity): Control with output feedback compensators using parameter optimization

    NASA Technical Reports Server (NTRS)

    Schoemig, Ewald; Ly, Uy-Loi

    1992-01-01

    Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.

  12. Mixed H2/H(infinity)-Control with an output-feedback compensator using parameter optimization

    NASA Technical Reports Server (NTRS)

    Schoemig, Ewald; Ly, Uy-Loi

    1992-01-01

    Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.

  13. 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.

  14. Optimal control of multiplicative control systems arising from cancer therapy

    NASA Technical Reports Server (NTRS)

    Bahrami, K.; Kim, M.

    1975-01-01

    This study deals with ways of curtailing the rapid growth of cancer cell populations. The performance functional that measures the size of the population at the terminal time as well as the control effort is devised. With use of the discrete maximum principle, the Hamiltonian for this problem is determined and the condition for optimal solutions are developed. The optimal strategy is shown to be a bang-bang control. It is shown that the optimal control for this problem must be on the vertices of an N-dimensional cube contained in the N-dimensional Euclidean space. An algorithm for obtaining a local minimum of the performance function in an orderly fashion is developed. Application of the algorithm to the design of antitumor drug and X-irradiation schedule is discussed.

  15. Digital program for solving the linear stochastic optimal control and estimation problem

    NASA Technical Reports Server (NTRS)

    Geyser, L. C.; Lehtinen, B.

    1975-01-01

    A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

  16. Artificial intelligence in robot control systems

    NASA Astrophysics Data System (ADS)

    Korikov, A.

    2018-05-01

    This paper analyzes modern concepts of artificial intelligence and known definitions of the term "level of intelligence". In robotics artificial intelligence system is defined as a system that works intelligently and optimally. The author proposes to use optimization methods for the design of intelligent robot control systems. The article provides the formalization of problems of robotic control system design, as a class of extremum problems with constraints. Solving these problems is rather complicated due to the high dimensionality, polymodality and a priori uncertainty. Decomposition of the extremum problems according to the method, suggested by the author, allows reducing them into a sequence of simpler problems, that can be successfully solved by modern computing technology. Several possible approaches to solving such problems are considered in the article.

  17. Occupant-responsive optimal control of smart facade systems

    NASA Astrophysics Data System (ADS)

    Park, Cheol-Soo

    Windows provide occupants with daylight, direct sunlight, visual contact with the outside and a feeling of openness. Windows enable the use of daylighting and offer occupants a outside view. Glazing may also cause a number of problems: undesired heat gain/loss in winter. An over-lit window can cause glare, which is another major complaint by occupants. Furthermore, cold or hot window surfaces induce asymmetric thermal radiation which can result in thermal discomfort. To reduce the potential problems of window systems, double skin facades and airflow window systems have been introduced in the 1970s. They typically contain interstitial louvers and ventilation openings. The current problem with double skin facades and airflow windows is that their operation requires adequate dynamic control to reach their expected performance. Many studies have recognized that only an optimal control enables these systems to truly act as active energy savers and indoor environment controllers. However, an adequate solution for this dynamic optimization problem has thus far not been developed. The primary objective of this study is to develop occupant responsive optimal control of smart facade systems. The control could be implemented as a smart controller that operates the motorized Venetian blind system and the opening ratio of ventilation openings. The objective of the control is to combine the benefits of large windows with low energy demands for heating and cooling, while keeping visual well-being and thermal comfort at an optimal level. The control uses a simulation model with an embedded optimization routine that allows occupant interaction via the Web. An occupant can access the smart controller from a standard browser and choose a pre-defined mode (energy saving mode, visual comfort mode, thermal comfort mode, default mode, nighttime mode) or set a preferred mode (user-override mode) by moving preference sliders on the screen. The most prominent feature of these systems is the capability of dynamically reacting to the environmental input data through real-time optimization. The proposed occupant responsive optimal control of smart facade systems could provide a breakthrough in this under-developed area and lead to a renewed interest in smart facade systems.

  18. Low thrust spacecraft transfers optimization method with the stepwise control structure in the Earth-Moon system in terms of the L1-L2 transfer

    NASA Astrophysics Data System (ADS)

    Fain, M. K.; Starinova, O. L.

    2016-04-01

    The paper outlines the method for determination of the locally optimal stepwise control structure in the problem of the low thrust spacecraft transfer optimization in the Earth-Moon system, including the L1-L2 transfer. The total flight time as an optimization criterion is considered. The optimal control programs were obtained by using the Pontryagin's maximum principle. As a result of optimization, optimal control programs, corresponding trajectories, and minimal total flight times were determined.

  19. Optimal control of information epidemics modeled as Maki Thompson rumors

    NASA Astrophysics Data System (ADS)

    Kandhway, Kundan; Kuri, Joy

    2014-12-01

    We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns.

  20. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    NASA Astrophysics Data System (ADS)

    Nørgaard, Sebastian; Sigmund, Ole; Lazarov, Boyan

    2016-02-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

  1. Simultaneous multislice refocusing via time optimal control.

    PubMed

    Rund, Armin; Aigner, Christoph Stefan; Kunisch, Karl; Stollberger, Rudolf

    2018-02-09

    Joint design of minimum duration RF pulses and slice-selective gradient shapes for MRI via time optimal control with strict physical constraints, and its application to simultaneous multislice imaging. The minimization of the pulse duration is cast as a time optimal control problem with inequality constraints describing the refocusing quality and physical constraints. It is solved with a bilevel method, where the pulse length is minimized in the upper level, and the constraints are satisfied in the lower level. To address the inherent nonconvexity of the optimization problem, the upper level is enhanced with new heuristics for finding a near global optimizer based on a second optimization problem. A large set of optimized examples shows an average temporal reduction of 87.1% for double diffusion and 74% for turbo spin echo pulses compared to power independent number of slices pulses. The optimized results are validated on a 3T scanner with phantom measurements. The presented design method computes minimum duration RF pulse and slice-selective gradient shapes subject to physical constraints. The shorter pulse duration can be used to decrease the effective echo time in existing echo-planar imaging or echo spacing in turbo spin echo sequences. © 2018 International Society for Magnetic Resonance in Medicine.

  2. Control Improvement for Jump-Diffusion Processes with Applications to Finance

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

    Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

    2012-02-15

    We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

  3. Multidisciplinary optimization of controlled space structures with global sensitivity equations

    NASA Technical Reports Server (NTRS)

    Padula, Sharon L.; James, Benjamin B.; Graves, Philip C.; Woodard, Stanley E.

    1991-01-01

    A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

  4. 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.

  5. Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

    NASA Astrophysics Data System (ADS)

    Burman, Erik; Hansbo, Peter; Larson, Mats G.

    2018-03-01

    Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

  6. Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.

    PubMed

    Patri, Jean-François; Diard, Julien; Perrier, Pascal

    2015-12-01

    The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.

  7. Aerospace applications of integer and combinatorial optimization

    NASA Technical Reports Server (NTRS)

    Padula, S. L.; Kincaid, R. K.

    1995-01-01

    Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

  8. Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

    NASA Astrophysics Data System (ADS)

    Shen, Kaiming; Yu, Wei

    2018-05-01

    This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave-convex FP problem--in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper.

  9. Effect of rotation rate on the forces of a rotating cylinder: Simulation and control

    NASA Technical Reports Server (NTRS)

    Burns, John A.; Ou, Yuh-Roung

    1993-01-01

    In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.

  10. Integrated structure/control law design by multilevel optimization

    NASA Technical Reports Server (NTRS)

    Gilbert, Michael G.; Schmidt, David K.

    1989-01-01

    A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

  11. Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

    PubMed

    Kiumarsi, Bahare; Lewis, Frank L

    2015-01-01

    This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

  12. The use of optimization techniques to design controlled diffusion compressor blading

    NASA Technical Reports Server (NTRS)

    Sanger, N. L.

    1982-01-01

    A method for automating compressor blade design using numerical optimization, and applied to the design of a controlled diffusion stator blade row is presented. A general purpose optimization procedure is employed, based on conjugate directions for locally unconstrained problems and on feasible directions for locally constrained problems. Coupled to the optimizer is an analysis package consisting of three analysis programs which calculate blade geometry, inviscid flow, and blade surface boundary layers. The optimizing concepts and selection of design objective and constraints are described. The procedure for automating the design of a two dimensional blade section is discussed, and design results are presented.

  13. Algorithm For Optimal Control Of Large Structures

    NASA Technical Reports Server (NTRS)

    Salama, Moktar A.; Garba, John A..; Utku, Senol

    1989-01-01

    Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

  14. Efficiency of quantum vs. classical annealing in nonconvex learning problems

    PubMed Central

    Zecchina, Riccardo

    2018-01-01

    Quantum annealers aim at solving nonconvex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists of designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of nonconvex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes are dominated by local minima that cause exponential slowdown of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions. PMID:29382764

  15. A System-Oriented Approach for the Optimal Control of Process Chains under Stochastic Influences

    NASA Astrophysics Data System (ADS)

    Senn, Melanie; Schäfer, Julian; Pollak, Jürgen; Link, Norbert

    2011-09-01

    Process chains in manufacturing consist of multiple connected processes in terms of dynamic systems. The properties of a product passing through such a process chain are influenced by the transformation of each single process. There exist various methods for the control of individual processes, such as classical state controllers from cybernetics or function mapping approaches realized by statistical learning. These controllers ensure that a desired state is obtained at process end despite of variations in the input and disturbances. The interactions between the single processes are thereby neglected, but play an important role in the optimization of the entire process chain. We divide the overall optimization into two phases: (1) the solution of the optimization problem by Dynamic Programming to find the optimal control variable values for each process for any encountered end state of its predecessor and (2) the application of the optimal control variables at runtime for the detected initial process state. The optimization problem is solved by selecting adequate control variables for each process in the chain backwards based on predefined quality requirements for the final product. For the demonstration of the proposed concept, we have chosen a process chain from sheet metal manufacturing with simplified transformation functions.

  16. Hybrid Optimization in Urban Traffic Networks

    DOT National Transportation Integrated Search

    1979-04-01

    The hybrid optimization problem is formulated to provide a general theoretical framework for the analysis of a class of traffic control problems which takes into account the role of individual drivers as independent decisionmakers. Different behavior...

  17. Improving stability margins in discrete-time LQG controllers

    NASA Technical Reports Server (NTRS)

    Oranc, B. Tarik; Phillips, Charles L.

    1987-01-01

    Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.

  18. Model Predictive Control-based Optimal Coordination of Distributed Energy Resources

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

    Mayhorn, Ebony T.; Kalsi, Karanjit; Lian, Jianming

    2013-01-07

    Distributed energy resources, such as renewable energy resources (wind, solar), energy storage and demand response, can be used to complement conventional generators. The uncertainty and variability due to high penetration of wind makes reliable system operations and controls challenging, especially in isolated systems. In this paper, an optimal control strategy is proposed to coordinate energy storage and diesel generators to maximize wind penetration while maintaining system economics and normal operation performance. The goals of the optimization problem are to minimize fuel costs and maximize the utilization of wind while considering equipment life of generators and energy storage. Model predictive controlmore » (MPC) is used to solve a look-ahead dispatch optimization problem and the performance is compared to an open loop look-ahead dispatch problem. Simulation studies are performed to demonstrate the efficacy of the closed loop MPC in compensating for uncertainties and variability caused in the system.« less

  19. Model Predictive Control-based Optimal Coordination of Distributed Energy Resources

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

    Mayhorn, Ebony T.; Kalsi, Karanjit; Lian, Jianming

    2013-04-03

    Distributed energy resources, such as renewable energy resources (wind, solar), energy storage and demand response, can be used to complement conventional generators. The uncertainty and variability due to high penetration of wind makes reliable system operations and controls challenging, especially in isolated systems. In this paper, an optimal control strategy is proposed to coordinate energy storage and diesel generators to maximize wind penetration while maintaining system economics and normal operation performance. The goals of the optimization problem are to minimize fuel costs and maximize the utilization of wind while considering equipment life of generators and energy storage. Model predictive controlmore » (MPC) is used to solve a look-ahead dispatch optimization problem and the performance is compared to an open loop look-ahead dispatch problem. Simulation studies are performed to demonstrate the efficacy of the closed loop MPC in compensating for uncertainties and variability caused in the system.« less

  20. An hp symplectic pseudospectral method for nonlinear optimal control

    NASA Astrophysics Data System (ADS)

    Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

    2017-01-01

    An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

  1. Distributed Control with Collective Intelligence

    NASA Technical Reports Server (NTRS)

    Wolpert, David H.; Wheeler, Kevin R.; Tumer, Kagan

    1998-01-01

    We consider systems of interacting reinforcement learning (RL) algorithms that do not work at cross purposes , in that their collective behavior maximizes a global utility function. We call such systems COllective INtelligences (COINs). We present the theory of designing COINs. Then we present experiments validating that theory in the context of two distributed control problems: We show that COINs perform near-optimally in a difficult variant of Arthur's bar problem [Arthur] (and in particular avoid the tragedy of the commons for that problem), and we also illustrate optimal performance in the master-slave problem.

  2. Optimizing the Usability of Brain-Computer Interfaces.

    PubMed

    Zhang, Yin; Chase, Steve M

    2018-05-01

    Brain-computer interfaces are in the process of moving from the laboratory to the clinic. These devices act by reading neural activity and using it to directly control a device, such as a cursor on a computer screen. An open question in the field is how to map neural activity to device movement in order to achieve the most proficient control. This question is complicated by the fact that learning, especially the long-term skill learning that accompanies weeks of practice, can allow subjects to improve performance over time. Typical approaches to this problem attempt to maximize the biomimetic properties of the device in order to limit the need for extensive training. However, it is unclear if this approach would ultimately be superior to performance that might be achieved with a nonbiomimetic device once the subject has engaged in extended practice and learned how to use it. Here we approach this problem using ideas from optimal control theory. Under the assumption that the brain acts as an optimal controller, we present a formal definition of the usability of a device and show that the optimal postlearning mapping can be written as the solution of a constrained optimization problem. We then derive the optimal mappings for particular cases common to most brain-computer interfaces. Our results suggest that the common approach of creating biomimetic interfaces may not be optimal when learning is taken into account. More broadly, our method provides a blueprint for optimal device design in general control-theoretic contexts.

  3. Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

    DTIC Science & Technology

    2018-03-14

    pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

  4. Multirate sampled-data yaw-damper and modal suppression system design

    NASA Technical Reports Server (NTRS)

    Berg, Martin C.; Mason, Gregory S.

    1990-01-01

    A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

  5. Non linear predictive control of a LEGO mobile robot

    NASA Astrophysics Data System (ADS)

    Merabti, H.; Bouchemal, B.; Belarbi, K.; Boucherma, D.; Amouri, A.

    2014-10-01

    Metaheuristics are general purpose heuristics which have shown a great potential for the solution of difficult optimization problems. In this work, we apply the meta heuristic, namely particle swarm optimization, PSO, for the solution of the optimization problem arising in NLMPC. This algorithm is easy to code and may be considered as alternatives for the more classical solution procedures. The PSO- NLMPC is applied to control a mobile robot for the tracking trajectory and obstacles avoidance. Experimental results show the strength of this approach.

  6. Hybrid Quantum-Classical Approach to Quantum Optimal Control.

    PubMed

    Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

    2017-04-14

    A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

  7. Active control of panel vibrations induced by boundary-layer flow

    NASA Technical Reports Server (NTRS)

    Chow, Pao-Liu

    1991-01-01

    Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

  8. Optimal Control and Smoothing Techniques for Computing Minimum Fuel Orbital Transfers and Rendezvous

    NASA Astrophysics Data System (ADS)

    Epenoy, R.; Bertrand, R.

    We investigate in this paper the computation of minimum fuel orbital transfers and rendezvous. Each problem is seen as an optimal control problem and is solved by means of shooting methods [1]. This approach corresponds to the use of Pontryagin's Maximum Principle (PMP) [2-4] and leads to the solution of a Two Point Boundary Value Problem (TPBVP). It is well known that this last one is very difficult to solve when the performance index is fuel consumption because in this case the optimal control law has a particular discontinuous structure called "bang-bang". We will show how to modify the performance index by a term depending on a small parameter in order to yield regular controls. Then, a continuation method on this parameter will lead us to the solution of the original problem. Convergence theorems will be given. Finally, numerical examples will illustrate the interest of our method. We will consider two particular problems: The GTO (Geostationary Transfer Orbit) to GEO (Geostationary Equatorial Orbit) transfer and the LEO (Low Earth Orbit) rendezvous.

  9. Integrated identification, modeling and control with applications

    NASA Astrophysics Data System (ADS)

    Shi, Guojun

    This thesis deals with the integration of system design, identification, modeling and control. In particular, six interdisciplinary engineering problems are addressed and investigated. Theoretical results are established and applied to structural vibration reduction and engine control problems. First, the data-based LQG control problem is formulated and solved. It is shown that a state space model is not necessary to solve this problem; rather a finite sequence from the impulse response is the only model data required to synthesize an optimal controller. The new theory avoids unnecessary reliance on a model, required in the conventional design procedure. The infinite horizon model predictive control problem is addressed for multivariable systems. The basic properties of the receding horizon implementation strategy is investigated and the complete framework for solving the problem is established. The new theory allows the accommodation of hard input constraints and time delays. The developed control algorithms guarantee the closed loop stability. A closed loop identification and infinite horizon model predictive control design procedure is established for engine speed regulation. The developed algorithms are tested on the Cummins Engine Simulator and desired results are obtained. A finite signal-to-noise ratio model is considered for noise signals. An information quality index is introduced which measures the essential information precision required for stabilization. The problems of minimum variance control and covariance control are formulated and investigated. Convergent algorithms are developed for solving the problems of interest. The problem of the integrated passive and active control design is addressed in order to improve the overall system performance. A design algorithm is developed, which simultaneously finds: (i) the optimal values of the stiffness and damping ratios for the structure, and (ii) an optimal output variance constrained stabilizing controller such that the active control energy is minimized. A weighted q-Markov COVER method is introduced for identification with measurement noise. The result is use to develop an iterative closed loop identification/control design algorithm. The effectiveness of the algorithm is illustrated by experimental results.

  10. Neural-network-based online HJB solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems.

    PubMed

    Liu, Derong; Wang, Ding; Wang, Fei-Yue; Li, Hongliang; Yang, Xiong

    2014-12-01

    In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.

  11. 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.

  12. 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

  13. 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.

  14. Network models for solving the problem of multicriterial adaptive optimization of investment projects control with several acceptable technologies

    NASA Astrophysics Data System (ADS)

    Shorikov, A. F.; Butsenko, E. V.

    2017-10-01

    This paper discusses the problem of multicriterial adaptive optimization the control of investment projects in the presence of several technologies. On the basis of network modeling proposed a new economic and mathematical model and a method for solving the problem of multicriterial adaptive optimization the control of investment projects in the presence of several technologies. Network economic and mathematical modeling allows you to determine the optimal time and calendar schedule for the implementation of the investment project and serves as an instrument to increase the economic potential and competitiveness of the enterprise. On a meaningful practical example, the processes of forming network models are shown, including the definition of the sequence of actions of a particular investment projecting process, the network-based work schedules are constructed. The calculation of the parameters of network models is carried out. Optimal (critical) paths have been formed and the optimal time for implementing the chosen technologies of the investment project has been calculated. It also shows the selection of the optimal technology from a set of possible technologies for project implementation, taking into account the time and cost of the work. The proposed model and method for solving the problem of managing investment projects can serve as a basis for the development, creation and application of appropriate computer information systems to support the adoption of managerial decisions by business people.

  15. Autorotation flight control system

    NASA Technical Reports Server (NTRS)

    Bachelder, Edward N. (Inventor); Aponso, Bimal L. (Inventor); Lee, Dong-Chan (Inventor)

    2011-01-01

    The present invention provides computer implemented methodology that permits the safe landing and recovery of rotorcraft following engine failure. With this invention successful autorotations may be performed from well within the unsafe operating area of the height-velocity profile of a helicopter by employing the fast and robust real-time trajectory optimization algorithm that commands control motion through an intuitive pilot display, or directly in the case of autonomous rotorcraft. The algorithm generates optimal trajectories and control commands via the direct-collocation optimization method, solved using a nonlinear programming problem solver. The control inputs computed are collective pitch and aircraft pitch, which are easily tracked and manipulated by the pilot or converted to control actuator commands for automated operation during autorotation in the case of an autonomous rotorcraft. The formulation of the optimal control problem has been carefully tailored so the solutions resemble those of an expert pilot, accounting for the performance limitations of the rotorcraft and safety concerns.

  16. $L^1$ penalization of volumetric dose objectives in optimal control of PDEs

    DOE PAGES

    Barnard, Richard C.; Clason, Christian

    2017-02-11

    This work is concerned with a class of PDE-constrained optimization problems that are motivated by an application in radiotherapy treatment planning. Here the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints leads to infeasible problems. We therefore propose an alternative approach based on L 1 penalization of the violation that is also applicable when state constraints are infeasible. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, discuss convergence of minimizers as the penalty parametermore » tends to infinity, and present a semismooth Newton method for their efficient numerical solution. Finally, the performance of this method for a model problem is illustrated and contrasted with an alternative approach based on (regularized) state constraints.« less

  17. Algorithms for output feedback, multiple-model, and decentralized control problems

    NASA Technical Reports Server (NTRS)

    Halyo, N.; Broussard, J. R.

    1984-01-01

    The optimal stochastic output feedback, multiple-model, and decentralized control problems with dynamic compensation are formulated and discussed. Algorithms for each problem are presented, and their relationship to a basic output feedback algorithm is discussed. An aircraft control design problem is posed as a combined decentralized, multiple-model, output feedback problem. A control design is obtained using the combined algorithm. An analysis of the design is presented.

  18. Implicit methods for efficient musculoskeletal simulation and optimal control

    PubMed Central

    van den Bogert, Antonie J.; Blana, Dimitra; Heinrich, Dieter

    2011-01-01

    The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers. PMID:22102983

  19. Optimal Control of Hybrid Systems in Air Traffic Applications

    NASA Astrophysics Data System (ADS)

    Kamgarpour, Maryam

    Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient implementation of the proposed algorithms.

  20. 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.

  1. A general optimality criteria algorithm for a class of engineering optimization problems

    NASA Astrophysics Data System (ADS)

    Belegundu, Ashok D.

    2015-05-01

    An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

  2. Optimal control problems with mixed control-phase variable equality and inequality constraints

    NASA Technical Reports Server (NTRS)

    Makowski, K.; Neustad, L. W.

    1974-01-01

    In this paper, necessary conditions are obtained for optimal control problems containing equality constraints defined in terms of functions of the control and phase variables. The control system is assumed to be characterized by an ordinary differential equation, and more conventional constraints, including phase inequality constraints, are also assumed to be present. Because the first-mentioned equality constraint must be satisfied for all t (the independent variable of the differential equation) belonging to an arbitrary (prescribed) measurable set, this problem gives rise to infinite-dimensional equality constraints. To obtain the necessary conditions, which are in the form of a maximum principle, an implicit-function-type theorem in Banach spaces is derived.

  3. Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

    NASA Technical Reports Server (NTRS)

    Aldrich, Jack B.; Okon, Avi B.

    2012-01-01

    The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

  4. Optimal Routing and Control of Multiple Agents Moving in a Transportation Network and Subject to an Arrival Schedule and Separation Constraints

    NASA Technical Reports Server (NTRS)

    Sadovsky, A. V.; Davis, D.; Isaacson, D. R.

    2012-01-01

    We address the problem of navigating a set of moving agents, e.g. automated guided vehicles, through a transportation network so as to bring each agent to its destination at a specified time. Each pair of agents is required to be separated by a minimal distance, generally agent-dependent, at all times. The speed range, initial position, required destination, and required time of arrival at destination for each agent are assumed provided. The movement of each agent is governed by a controlled differential equation (state equation). The problem consists in choosing for each agent a path and a control strategy so as to meet the constraints and reach the destination at the required time. This problem arises in various fields of transportation, including Air Traffic Management and train coordination, and in robotics. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver.

  5. 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.

  6. A finite element based method for solution of optimal control problems

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

    A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

  7. Optimal starting conditions for the rendezvous maneuver: Analytical and computational approach

    NASA Astrophysics Data System (ADS)

    Ciarcia, Marco

    The three-dimensional rendezvous between two spacecraft is considered: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft. The above problem has been studied by several authors under the assumption that the initial separation coordinates and the initial separation velocities are given, hence known initial conditions for the chaser spacecraft. In this paper, it is assumed that both the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given so as to prevent the occurrence of trivial solutions. Two approaches are employed: optimal control formulation (Part A) and mathematical programming formulation (Part B). In Part A, analyses are performed with the multiple-subarc sequential gradient-restoration algorithm for optimal control problems. They show that the fuel-optimal trajectory is zero-bang, namely it is characterized by two subarcs: a long coasting zero-thrust subarc followed by a short powered max-thrust braking subarc. While the thrust direction of the powered subarc is continuously variable for the optimal trajectory, its replacement with a constant (yet optimized) thrust direction produces a very efficient guidance trajectory. Indeed, for all values of the initial distance, the fuel required by the guidance trajectory is within less than one percent of the fuel required by the optimal trajectory. For the guidance trajectory, because of the replacement of the variable thrust direction of the powered subarc with a constant thrust direction, the optimal control problem degenerates into a mathematical programming problem with a relatively small number of degrees of freedom, more precisely: three for case (i) time-to-rendezvous free and two for case (ii) time-to-rendezvous given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory. In Part B, an analytical solution of the Clohessy-Wiltshire equations is presented (i) neglecting the change of the spacecraft mass due to the fuel consumption and (ii) and assuming that the thrust is finite, that is, the trajectory includes powered subarcs flown with max thrust and coasting subarc flown with zero thrust. Then, employing the found analytical solution, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. The main contribution of Part B is the development of analytical solutions for the powered subarcs, an important extension of the analytical solutions already available for the coasting subarcs. One consequence is that the entire optimal trajectory can be described analytically. Another consequence is that the optimal control problems degenerate into mathematical programming problems. A further consequence is that, vis-a-vis the optimal control formulation, the mathematical programming formulation reduces the CPU time by a factor of order 1000. Key words. Space trajectories, rendezvous, optimization, guidance, optimal control, calculus of variations, Mayer problems, Bolza problems, transformation techniques, multiple-subarc sequential gradient-restoration algorithm.

  8. Generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB.

    PubMed

    Lee, Leng-Feng; Umberger, Brian R

    2016-01-01

    Computer modeling, simulation and optimization are powerful tools that have seen increased use in biomechanics research. Dynamic optimizations can be categorized as either data-tracking or predictive problems. The data-tracking approach has been used extensively to address human movement problems of clinical relevance. The predictive approach also holds great promise, but has seen limited use in clinical applications. Enhanced software tools would facilitate the application of predictive musculoskeletal simulations to clinically-relevant research. The open-source software OpenSim provides tools for generating tracking simulations but not predictive simulations. However, OpenSim includes an extensive application programming interface that permits extending its capabilities with scripting languages such as MATLAB. In the work presented here, we combine the computational tools provided by MATLAB with the musculoskeletal modeling capabilities of OpenSim to create a framework for generating predictive simulations of musculoskeletal movement based on direct collocation optimal control techniques. In many cases, the direct collocation approach can be used to solve optimal control problems considerably faster than traditional shooting methods. Cyclical and discrete movement problems were solved using a simple 1 degree of freedom musculoskeletal model and a model of the human lower limb, respectively. The problems could be solved in reasonable amounts of time (several seconds to 1-2 hours) using the open-source IPOPT solver. The problems could also be solved using the fmincon solver that is included with MATLAB, but the computation times were excessively long for all but the smallest of problems. The performance advantage for IPOPT was derived primarily by exploiting sparsity in the constraints Jacobian. The framework presented here provides a powerful and flexible approach for generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB. This should allow researchers to more readily use predictive simulation as a tool to address clinical conditions that limit human mobility.

  9. Generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB

    PubMed Central

    Lee, Leng-Feng

    2016-01-01

    Computer modeling, simulation and optimization are powerful tools that have seen increased use in biomechanics research. Dynamic optimizations can be categorized as either data-tracking or predictive problems. The data-tracking approach has been used extensively to address human movement problems of clinical relevance. The predictive approach also holds great promise, but has seen limited use in clinical applications. Enhanced software tools would facilitate the application of predictive musculoskeletal simulations to clinically-relevant research. The open-source software OpenSim provides tools for generating tracking simulations but not predictive simulations. However, OpenSim includes an extensive application programming interface that permits extending its capabilities with scripting languages such as MATLAB. In the work presented here, we combine the computational tools provided by MATLAB with the musculoskeletal modeling capabilities of OpenSim to create a framework for generating predictive simulations of musculoskeletal movement based on direct collocation optimal control techniques. In many cases, the direct collocation approach can be used to solve optimal control problems considerably faster than traditional shooting methods. Cyclical and discrete movement problems were solved using a simple 1 degree of freedom musculoskeletal model and a model of the human lower limb, respectively. The problems could be solved in reasonable amounts of time (several seconds to 1–2 hours) using the open-source IPOPT solver. The problems could also be solved using the fmincon solver that is included with MATLAB, but the computation times were excessively long for all but the smallest of problems. The performance advantage for IPOPT was derived primarily by exploiting sparsity in the constraints Jacobian. The framework presented here provides a powerful and flexible approach for generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB. This should allow researchers to more readily use predictive simulation as a tool to address clinical conditions that limit human mobility. PMID:26835184

  10. Optimal Control of Distributed Energy Resources using Model Predictive Control

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

    Mayhorn, Ebony T.; Kalsi, Karanjit; Elizondo, Marcelo A.

    2012-07-22

    In an isolated power system (rural microgrid), Distributed Energy Resources (DERs) such as renewable energy resources (wind, solar), energy storage and demand response can be used to complement fossil fueled generators. The uncertainty and variability due to high penetration of wind makes reliable system operations and controls challenging. In this paper, an optimal control strategy is proposed to coordinate energy storage and diesel generators to maximize wind penetration while maintaining system economics and normal operation. The problem is formulated as a multi-objective optimization problem with the goals of minimizing fuel costs and changes in power output of diesel generators, minimizingmore » costs associated with low battery life of energy storage and maintaining system frequency at the nominal operating value. Two control modes are considered for controlling the energy storage to compensate either net load variability or wind variability. Model predictive control (MPC) is used to solve the aforementioned problem and the performance is compared to an open-loop look-ahead dispatch problem. Simulation studies using high and low wind profiles, as well as, different MPC prediction horizons demonstrate the efficacy of the closed-loop MPC in compensating for uncertainties in wind and demand.« less

  11. Optimal Protocols and Optimal Transport in Stochastic Thermodynamics

    NASA Astrophysics Data System (ADS)

    Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2011-06-01

    Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

  12. Optimal protocols and optimal transport in stochastic thermodynamics.

    PubMed

    Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2011-06-24

    Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

  13. A problem of optimal control and observation for distributed homogeneous multi-agent system

    NASA Astrophysics Data System (ADS)

    Kruglikov, Sergey V.

    2017-12-01

    The paper considers the implementation of a algorithm for controlling a distributed complex of several mobile multi-robots. The concept of a unified information space of the controlling system is applied. The presented information and mathematical models of participants and obstacles, as real agents, and goals and scenarios, as virtual agents, create the base forming the algorithmic and software background for computer decision support system. The controlling scheme assumes the indirect management of the robotic team on the basis of optimal control and observation problem predicting intellectual behavior in a dynamic, hostile environment. A basic content problem is a compound cargo transportation by a group of participants in the case of a distributed control scheme in the terrain with multiple obstacles.

  14. Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

    NASA Astrophysics Data System (ADS)

    Li, Guang

    2017-01-01

    This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

  15. Optimal Culling and Biocontrol in a Predator-Prey Model.

    PubMed

    Numfor, Eric; Hilker, Frank M; Lenhart, Suzanne

    2017-01-01

    Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward-backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.

  16. 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.

  17. Coordinated control of active and reactive power of distribution network with distributed PV cluster via model predictive control

    NASA Astrophysics Data System (ADS)

    Ji, Yu; Sheng, Wanxing; Jin, Wei; Wu, Ming; Liu, Haitao; Chen, Feng

    2018-02-01

    A coordinated optimal control method of active and reactive power of distribution network with distributed PV cluster based on model predictive control is proposed in this paper. The method divides the control process into long-time scale optimal control and short-time scale optimal control with multi-step optimization. The models are transformed into a second-order cone programming problem due to the non-convex and nonlinear of the optimal models which are hard to be solved. An improved IEEE 33-bus distribution network system is used to analyse the feasibility and the effectiveness of the proposed control method

  18. Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

    NASA Technical Reports Server (NTRS)

    Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

    1990-01-01

    The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

  19. Forecasting Electricity Prices in an Optimization Hydrothermal Problem

    NASA Astrophysics Data System (ADS)

    Matías, J. M.; Bayón, L.; Suárez, P.; Argüelles, A.; Taboada, J.

    2007-12-01

    This paper presents an economic dispatch algorithm in a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of one firm is described, whose objective function can be defined as its profit maximization. Since next-day price forecasting is an aspect crucial, this paper proposes an efficient yet highly accurate next-day price new forecasting method using a functional time series approach trying to exploit the daily seasonal structure of the series of prices. For the optimization problem, an optimal control technique is applied and Pontryagin's theorem is employed.

  20. Aerospace Applications of Integer and Combinatorial Optimization

    NASA Technical Reports Server (NTRS)

    Padula, S. L.; Kincaid, R. K.

    1995-01-01

    Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

  1. Aerospace applications on integer and combinatorial optimization

    NASA Technical Reports Server (NTRS)

    Padula, S. L.; Kincaid, R. K.

    1995-01-01

    Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

  2. Integrated Controls-Structures Design Methodology for Flexible Spacecraft

    NASA Technical Reports Server (NTRS)

    Maghami, P. G.; Joshi, S. M.; Price, D. B.

    1995-01-01

    This paper proposes an approach for the design of flexible spacecraft, wherein the structural design and the control system design are performed simultaneously. The integrated design problem is posed as an optimization problem in which both the structural parameters and the control system parameters constitute the design variables, which are used to optimize a common objective function, thereby resulting in an optimal overall design. The approach is demonstrated by application to the integrated design of a geostationary platform, and to a ground-based flexible structure experiment. The numerical results obtained indicate that the integrated design approach generally yields spacecraft designs that are substantially superior to the conventional approach, wherein the structural design and control design are performed sequentially.

  3. Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

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

    Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Piunovskiy, A. B., E-mail: piunov@liv.ac.uk

    2016-08-15

    In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures ofmore » the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.« less

  4. Existence and characterization of optimal control in mathematics model of diabetics population

    NASA Astrophysics Data System (ADS)

    Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

    2018-03-01

    Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

  5. On the existence of touch points for first-order state inequality constraints

    NASA Technical Reports Server (NTRS)

    Seywald, Hans; Cliff, Eugene M.

    1993-01-01

    The appearance of touch points in state constrained optimal control problems with general vector-valued control is studied. Under the assumption that the Hamiltonian is regular, touch points for first-order state inequalities are shown to exist only under very special conditions. In many cases of practical importance these conditions can be used to exclude touch points a priori without solving an optimal control problem. The results are demonstrated on a simple example.

  6. Computationally efficient control allocation

    NASA Technical Reports Server (NTRS)

    Durham, Wayne (Inventor)

    2001-01-01

    A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

  7. Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

    NASA Astrophysics Data System (ADS)

    Sardesai, Chetan R.

    The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

  8. 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.

  9. Control of functional differential equations with function space boundary conditions

    NASA Technical Reports Server (NTRS)

    Banks, H. T.

    1972-01-01

    Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported.

  10. Optimal lunar soft landing trajectories using taboo evolutionary programming

    NASA Astrophysics Data System (ADS)

    Mutyalarao, M.; Raj, M. Xavier James

    A safe lunar landing is a key factor to undertake an effective lunar exploration. Lunar lander consists of four phases such as launch phase, the earth-moon transfer phase, circumlunar phase and landing phase. The landing phase can be either hard landing or soft landing. Hard landing means the vehicle lands under the influence of gravity without any deceleration measures. However, soft landing reduces the vertical velocity of the vehicle before landing. Therefore, for the safety of the astronauts as well as the vehicle lunar soft landing with an acceptable velocity is very much essential. So it is important to design the optimal lunar soft landing trajectory with minimum fuel consumption. Optimization of Lunar Soft landing is a complex optimal control problem. In this paper, an analysis related to lunar soft landing from a parking orbit around Moon has been carried out. A two-dimensional trajectory optimization problem is attempted. The problem is complex due to the presence of system constraints. To solve the time-history of control parameters, the problem is converted into two point boundary value problem by using the maximum principle of Pontrygen. Taboo Evolutionary Programming (TEP) technique is a stochastic method developed in recent years and successfully implemented in several fields of research. It combines the features of taboo search and single-point mutation evolutionary programming. Identifying the best unknown parameters of the problem under consideration is the central idea for many space trajectory optimization problems. The TEP technique is used in the present methodology for the best estimation of initial unknown parameters by minimizing objective function interms of fuel requirements. The optimal estimation subsequently results into an optimal trajectory design of a module for soft landing on the Moon from a lunar parking orbit. Numerical simulations demonstrate that the proposed approach is highly efficient and it reduces the minimum fuel consumption. The results are compared with the available results in literature shows that the solution of present algorithm is better than some of the existing algorithms. Keywords: soft landing, trajectory optimization, evolutionary programming, control parameters, Pontrygen principle.

  11. Optimization of Systems with Uncertainty: Initial Developments for Performance, Robustness and Reliability Based Designs

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    This paper presents a study on the optimization of systems with structured uncertainties, whose inputs and outputs can be exhaustively described in the probabilistic sense. By propagating the uncertainty from the input to the output in the space of the probability density functions and the moments, optimization problems that pursue performance, robustness and reliability based designs are studied. Be specifying the desired outputs in terms of desired probability density functions and then in terms of meaningful probabilistic indices, we settle a computationally viable framework for solving practical optimization problems. Applications to static optimization and stability control are used to illustrate the relevance of incorporating uncertainty in the early stages of the design. Several examples that admit a full probabilistic description of the output in terms of the design variables and the uncertain inputs are used to elucidate the main features of the generic problem and its solution. Extensions to problems that do not admit closed form solutions are also evaluated. Concrete evidence of the importance of using a consistent probabilistic formulation of the optimization problem and a meaningful probabilistic description of its solution is provided in the examples. In the stability control problem the analysis shows that standard deterministic approaches lead to designs with high probability of running into instability. The implementation of such designs can indeed have catastrophic consequences.

  12. 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

  13. An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm.

    PubMed

    Deb, Kalyanmoy; Sinha, Ankur

    2010-01-01

    Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

  14. Optimal solution and optimality condition of the Hunter-Saxton equation

    NASA Astrophysics Data System (ADS)

    Shen, Chunyu

    2018-02-01

    This paper is devoted to the optimal distributed control problem governed by the Hunter-Saxton equation with constraints on the control. We first investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary conditions. In contrast with our previous research, the proof of solution mapping is local Lipschitz continuous, which is one big improvement. Second, based on the well-posedness result, we find a unique optimal control and optimal solution for the controlled system with the quadratic cost functional. Moreover, we establish the sufficient and necessary optimality condition of an optimal control by means of the optimal control theory, not limited to the necessary condition, which is another major novelty of this paper. We also discuss the optimality conditions corresponding to two physical meaningful distributed observation cases.

  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. Optimal blood glucose level control using dynamic programming based on minimal Bergman model

    NASA Astrophysics Data System (ADS)

    Rettian Anggita Sari, Maria; Hartono

    2018-03-01

    The purpose of this article is to simulate the glucose dynamic and the insulin kinetic of diabetic patient. The model used in this research is a non-linear Minimal Bergman model. Optimal control theory is then applied to formulate the problem in order to determine the optimal dose of insulin in the treatment of diabetes mellitus such that the glucose level is in the normal range for some specific time range. The optimization problem is solved using dynamic programming. The result shows that dynamic programming is quite reliable to represent the interaction between glucose and insulin levels in diabetes mellitus patient.

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

    Stroemqvist, Martin H., E-mail: stromqv@kth.se

    We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly onmore » the rate at which the size of the holes shrink.« less

  18. Optimal Full Information Synthesis for Flexible Structures Implemented on Cray Supercomputers

    NASA Technical Reports Server (NTRS)

    Lind, Rick; Balas, Gary J.

    1995-01-01

    This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.

  19. Regulation of Dynamical Systems to Optimal Solutions of Semidefinite Programs: Algorithms and Applications to AC Optimal Power Flow

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

    Dall'Anese, Emiliano; Dhople, Sairaj V.; Giannakis, Georgios B.

    2015-07-01

    This paper considers a collection of networked nonlinear dynamical systems, and addresses the synthesis of feedback controllers that seek optimal operating points corresponding to the solution of pertinent network-wide optimization problems. Particular emphasis is placed on the solution of semidefinite programs (SDPs). The design of the feedback controller is grounded on a dual e-subgradient approach, with the dual iterates utilized to dynamically update the dynamical-system reference signals. Global convergence is guaranteed for diminishing stepsize rules, even when the reference inputs are updated at a faster rate than the dynamical-system settling time. The application of the proposed framework to the controlmore » of power-electronic inverters in AC distribution systems is discussed. The objective is to bridge the time-scale separation between real-time inverter control and network-wide optimization. Optimization objectives assume the form of SDP relaxations of prototypical AC optimal power flow problems.« less

  20. Performance Optimizing Adaptive Control with Time-Varying Reference Model Modification

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Hashemi, Kelley E.

    2017-01-01

    This paper presents a new adaptive control approach that involves a performance optimization objective. The control synthesis involves the design of a performance optimizing adaptive controller from a subset of control inputs. The resulting effect of the performance optimizing adaptive controller is to modify the initial reference model into a time-varying reference model which satisfies the performance optimization requirement obtained from an optimal control problem. The time-varying reference model modification is accomplished by the real-time solutions of the time-varying Riccati and Sylvester equations coupled with the least-squares parameter estimation of the sensitivities of the performance metric. The effectiveness of the proposed method is demonstrated by an application of maneuver load alleviation control for a flexible aircraft.

  1. Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization.

    PubMed

    Li, Zhijun; Xia, Yuanqing; Su, Chun-Yi; Deng, Jun; Fu, Jun; He, Wei

    2015-08-01

    In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

  2. A Dynamic Process Model for Optimizing the Hospital Environment Cash-Flow

    NASA Astrophysics Data System (ADS)

    Pater, Flavius; Rosu, Serban

    2011-09-01

    In this article is presented a new approach to some fundamental techniques of solving dynamic programming problems with the use of functional equations. We will analyze the problem of minimizing the cost of treatment in a hospital environment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon.

  3. Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

    PubMed

    Wang, Xinghu; Hong, Yiguang; Ji, Haibo

    2016-07-01

    The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

  4. Numerical research of the optimal control problem in the semi-Markov inventory model

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

    Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.

    2015-03-10

    This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.

  5. Existence of Optimal Controls for Compressible Viscous Flow

    NASA Astrophysics Data System (ADS)

    Doboszczak, Stefan; Mohan, Manil T.; Sritharan, Sivaguru S.

    2018-03-01

    We formulate a control problem for a distributed parameter system where the state is governed by the compressible Navier-Stokes equations. Introducing a suitable cost functional, the existence of an optimal control is established within the framework of strong solutions in three dimensions.

  6. Optimal Output Trajectory Redesign for Invertible Systems

    NASA Technical Reports Server (NTRS)

    Devasia, S.

    1996-01-01

    Given a desired output trajectory, inversion-based techniques find input-state trajectories required to exactly track the output. These inversion-based techniques have been successfully applied to the endpoint tracking control of multijoint flexible manipulators and to aircraft control. The specified output trajectory uniquely determines the required input and state trajectories that are found through inversion. These input-state trajectories exactly track the desired output; however, they might not meet acceptable performance requirements. For example, during slewing maneuvers of flexible structures, the structural deformations, which depend on the required state trajectories, may be unacceptably large. Further, the required inputs might cause actuator saturation during an exact tracking maneuver, for example, in the flight control of conventional takeoff and landing aircraft. In such situations, a compromise is desired between the tracking requirement and other goals such as reduction of internal vibrations and prevention of actuator saturation; the desired output trajectory needs to redesigned. Here, we pose the trajectory redesign problem as an optimization of a general quadratic cost function and solve it in the context of linear systems. The solution is obtained as an off-line prefilter of the desired output trajectory. An advantage of our technique is that the prefilter is independent of the particular trajectory. The prefilter can therefore be precomputed, which is a major advantage over other optimization approaches. Previous works have addressed the issue of preshaping inputs to minimize residual and in-maneuver vibrations for flexible structures; Since the command preshaping is computed off-line. Further minimization of optimal quadratic cost functions has also been previously use to preshape command inputs for disturbance rejection. All of these approaches are applicable when the inputs to the system are known a priori. Typically, outputs (not inputs) are specified in tracking problems, and hence the input trajectories have to be computed. The inputs to the system are however, difficult to determine for non-minimum phase systems like flexible structures. One approach to solve this problem is to (1) choose a tracking controller (the desired output trajectory is now an input to the closed-loop system and (2) redesign this input to the closed-loop system. Thus we effectively perform output redesign. These redesigns are however, dependent on the choice of the tracking controllers. Thus the controller optimization and trajectory redesign problems become coupled; this coupled optimization is still an open problem. In contrast, we decouple the trajectory redesign problem from the choice of feedback-based tracking controller. It is noted that our approach remains valid when a particular tracking controller is chosen. In addition, the formulation of our problem not only allows for the minimization of residual vibration as in available techniques but also allows for the optimal reduction fo vibrations during the maneuver, e.g., the altitude control of flexible spacecraft. We begin by formulating the optimal output trajectory redesign problem and then solve it in the context of general linear systems. This theory is then applied to an example flexible structure, and simulation results are provided.

  7. Dynamic optimization approach for integrated supplier selection and tracking control of single product inventory system with product discount

    NASA Astrophysics Data System (ADS)

    Sutrisno; Widowati; Heru Tjahjana, R.

    2017-01-01

    In this paper, we propose a mathematical model in the form of dynamic/multi-stage optimization to solve an integrated supplier selection problem and tracking control problem of single product inventory system with product discount. The product discount will be stated as a piece-wise linear function. We use dynamic programming to solve this proposed optimization to determine the optimal supplier and the optimal product volume that will be purchased from the optimal supplier for each time period so that the inventory level tracks a reference trajectory given by decision maker with minimal total cost. We give a numerical experiment to evaluate the proposed model. From the result, the optimal supplier was determined for each time period and the inventory level follows the given reference well.

  8. Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

    PubMed

    Arrieta-Camacho, Juan José; Biegler, Lorenz T

    2005-12-01

    Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

  9. 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.

  10. Surrogate assisted multidisciplinary design optimization for an all-electric GEO satellite

    NASA Astrophysics Data System (ADS)

    Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian; Yuan, Bin

    2017-09-01

    State-of-the-art all-electric geostationary earth orbit (GEO) satellites use electric thrusters to execute all propulsive duties, which significantly differ from the traditional all-chemical ones in orbit-raising, station-keeping, radiation damage protection, and power budget, etc. Design optimization task of an all-electric GEO satellite is therefore a complex multidisciplinary design optimization (MDO) problem involving unique design considerations. However, solving the all-electric GEO satellite MDO problem faces big challenges in disciplinary modeling techniques and efficient optimization strategy. To address these challenges, we presents a surrogate assisted MDO framework consisting of several modules, i.e., MDO problem definition, multidisciplinary modeling, multidisciplinary analysis (MDA), and surrogate assisted optimizer. Based on the proposed framework, the all-electric GEO satellite MDO problem is formulated to minimize the total mass of the satellite system under a number of practical constraints. Then considerable efforts are spent on multidisciplinary modeling involving geosynchronous transfer, GEO station-keeping, power, thermal control, attitude control, and structure disciplines. Since orbit dynamics models and finite element structural model are computationally expensive, an adaptive response surface surrogate based optimizer is incorporated in the proposed framework to solve the satellite MDO problem with moderate computational cost, where a response surface surrogate is gradually refined to represent the computationally expensive MDA process. After optimization, the total mass of the studied GEO satellite is decreased by 185.3 kg (i.e., 7.3% of the total mass). Finally, the optimal design is further discussed to demonstrate the effectiveness of our proposed framework to cope with the all-electric GEO satellite system design optimization problems. This proposed surrogate assisted MDO framework can also provide valuable references for other all-electric spacecraft system design.

  11. Advances in optimal routing through computer networks

    NASA Technical Reports Server (NTRS)

    Paz, I. M.

    1977-01-01

    The optimal routing problem is defined. Progress in solving the problem during the previous decade is reviewed, with special emphasis on technical developments made during the last few years. The relationships between the routing, the throughput, and the switching technology used are discussed and their future trends are reviewed. Economic aspects are also briefly considered. Modern technical approaches for handling the routing problems and, more generally, the flow control problems are reviewed.

  12. 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.

  13. Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Ku, R. T.

    1972-01-01

    The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

  14. PID controller tuning using metaheuristic optimization algorithms for benchmark problems

    NASA Astrophysics Data System (ADS)

    Gholap, Vishal; Naik Dessai, Chaitali; Bagyaveereswaran, V.

    2017-11-01

    This paper contributes to find the optimal PID controller parameters using particle swarm optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm. The algorithms were developed through simulation of chemical process and electrical system and the PID controller is tuned. Here, two different fitness functions such as Integral Time Absolute Error and Time domain Specifications were chosen and applied on PSO, GA and SA while tuning the controller. The proposed Algorithms are implemented on two benchmark problems of coupled tank system and DC motor. Finally, comparative study has been done with different algorithms based on best cost, number of iterations and different objective functions. The closed loop process response for each set of tuned parameters is plotted for each system with each fitness function.

  15. 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.

  16. 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.

  17. Optimal Ventilation Control in Complex Urban Tunnels with Multi-Point Pollutant Discharge

    DOT National Transportation Integrated Search

    2017-10-01

    Zhen Tan (ORCID ID 0000-0003-1711-3557) H. Oliver Gao (ORCID ID 0000-0002-7861-9634) We propose an optimal ventilation control model for complex urban vehicular tunnels with distributed pollutant discharge points. The control problem is formulated as...

  18. 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.

  19. Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

    NASA Technical Reports Server (NTRS)

    Garcia, F., Jr.

    1974-01-01

    A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

  20. 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.

  1. On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads

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

    Li, Sen; Zhang, Wei; Lian, Jianming

    This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game bymore » connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.« less

  2. Compromise solution in the problem of change state control for the material body exposed to the external medium

    NASA Astrophysics Data System (ADS)

    Malafeyev, O. A.; Redinskikh, N. D.

    2018-05-01

    The problem of finding optimal temperature control of the material body state under the unknown in advance parameters of the external medium is formalized and studied in this paper. The problems of this type arise frequently in the real life. An optimal thermal regime is necessary to apply at the soil thawing or freezing, drying the building materials, heating the concrete to obtain the required strength, and so on. Problems of such type one can analyze making use the apparatus and methods of game theory. For describing the influence of external medium on the characteristics of different materials we make use the many-step two person zero-sum game in this paper. The compromise solution is taken as the optimality principle. The numerical example is given.

  3. Cascaded Optimization for a Persistent Data Ferrying Unmanned Aircraft

    NASA Astrophysics Data System (ADS)

    Carfang, Anthony

    This dissertation develops and assesses a cascaded method for designing optimal periodic trajectories and link schedules for an unmanned aircraft to ferry data between stationary ground nodes. This results in a fast solution method without the need to artificially constrain system dynamics. Focusing on a fundamental ferrying problem that involves one source and one destination, but includes complex vehicle and Radio-Frequency (RF) dynamics, a cascaded structure to the system dynamics is uncovered. This structure is exploited by reformulating the nonlinear optimization problem into one that reduces the independent control to the vehicle's motion, while the link scheduling control is folded into the objective function and implemented as an optimal policy that depends on candidate motion control. This formulation is proven to maintain optimality while reducing computation time in comparison to traditional ferry optimization methods. The discrete link scheduling problem takes the form of a combinatorial optimization problem that is known to be NP-Hard. A derived necessary condition for optimality guides the development of several heuristic algorithms, specifically the Most-Data-First Algorithm and the Knapsack Adaptation. These heuristics are extended to larger ferrying scenarios, and assessed analytically and through Monte Carlo simulation, showing better throughput performance in the same order of magnitude of computation time in comparison to other common link scheduling policies. The cascaded optimization method is implemented with a novel embedded software system on a small, unmanned aircraft to validate the simulation results with field experiments. To address the sensitivity of results on trajectory tracking performance, a system that combines motion and link control with waypoint-based navigation is developed and assessed through field experiments. The data ferrying algorithms are further extended by incorporating a Gaussian process to opportunistically learn the RF environment. By continuously improving RF models, the cascaded planner can continually improve the ferrying system's overall performance.

  4. Multimodel methods for optimal control of aeroacoustics.

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

    Chen, Guoquan; Collis, Samuel Scott

    2005-01-01

    A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully appliedmore » to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.« less

  5. Solvability of some partial functional integrodifferential equations with finite delay and optimal controls in Banach spaces.

    PubMed

    Ezzinbi, Khalil; Ndambomve, Patrice

    2016-01-01

    In this work, we consider the control system governed by some partial functional integrodifferential equations with finite delay in Banach spaces. We assume that the undelayed part admits a resolvent operator in the sense of Grimmer. Firstly, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of partial functional integrodifferential infinite dimensional control systems. Secondly, it is proved that, under generally mild conditions of cost functional, the associated Lagrange problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies. Our results extend and complement many other important results in the literature. Finally, a concrete example of application is given to illustrate the effectiveness of our main results.

  6. An optimal control method for fluid structure interaction systems via adjoint boundary pressure

    NASA Astrophysics Data System (ADS)

    Chirco, L.; Da Vià, R.; Manservisi, S.

    2017-11-01

    In recent year, in spite of the computational complexity, Fluid-structure interaction (FSI) problems have been widely studied due to their applicability in science and engineering. Fluid-structure interaction systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow. FSI simulations evaluate the tensional state of the mechanical component and take into account the effects of the solid deformations on the motion of the interior fluids. The inverse FSI problem can be described as the achievement of a certain objective by changing some design parameters such as forces, boundary conditions and geometrical domain shapes. In this paper we would like to study the inverse FSI problem by using an optimal control approach. In particular we propose a pressure boundary optimal control method based on Lagrangian multipliers and adjoint variables. The objective is the minimization of a solid domain displacement matching functional obtained by finding the optimal pressure on the inlet boundary. The optimality system is derived from the first order necessary conditions by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. The optimal solution is then obtained through a standard steepest descent algorithm applied to the optimality system. The approach presented in this work is general and could be used to assess other objective functionals and controls. In order to support the proposed approach we perform a few numerical tests where the fluid pressure on the domain inlet controls the displacement that occurs in a well defined region of the solid domain.

  7. Optimal dynamic control of resources in a distributed system

    NASA Technical Reports Server (NTRS)

    Shin, Kang G.; Krishna, C. M.; Lee, Yann-Hang

    1989-01-01

    The authors quantitatively formulate the problem of controlling resources in a distributed system so as to optimize a reward function and derive optimal control strategies using Markov decision theory. The control variables treated are quite general; they could be control decisions related to system configuration, repair, diagnostics, files, or data. Two algorithms for resource control in distributed systems are derived for time-invariant and periodic environments, respectively. A detailed example to demonstrate the power and usefulness of the approach is provided.

  8. Evolutionary Optimization of a Geometrically Refined Truss

    NASA Technical Reports Server (NTRS)

    Hull, P. V.; Tinker, M. L.; Dozier, G. V.

    2007-01-01

    Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

  9. Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

    NASA Astrophysics Data System (ADS)

    Pinson, Robin Marie

    Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

  10. Unification theory of optimal life histories and linear demographic models in internal stochasticity.

    PubMed

    Oizumi, Ryo

    2014-01-01

    Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

  11. Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

    PubMed Central

    Oizumi, Ryo

    2014-01-01

    Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

  12. Enabling Controlling Complex Networks with Local Topological Information.

    PubMed

    Li, Guoqi; Deng, Lei; Xiao, Gaoxi; Tang, Pei; Wen, Changyun; Hu, Wuhua; Pei, Jing; Shi, Luping; Stanley, H Eugene

    2018-03-15

    Complex networks characterize the nature of internal/external interactions in real-world systems including social, economic, biological, ecological, and technological networks. Two issues keep as obstacles to fulfilling control of large-scale networks: structural controllability which describes the ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost for driving the network to a predefined state with a given number of control inputs. For large complex networks without global information of network topology, both problems remain essentially open. Here we combine graph theory and control theory for tackling the two problems in one go, using only local network topology information. For the structural controllability problem, a distributed local-game matching method is proposed, where every node plays a simple Bayesian game with local information and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity. Starring from any structural controllability solution, a minimizing longest control path method can efficiently reach a good solution for the optimal control in large networks. Our results provide solutions for distributed complex network control and demonstrate a way to link the structural controllability and optimal control together.

  13. Pseudo-spectral control of a novel oscillating surge wave energy converter in regular waves for power optimization including load reduction

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

    Tom, Nathan M.; Yu, Yi -Hsiang; Wright, Alan D.

    The aim of this study is to describe a procedure to maximize the power-to-load ratio of a novel wave energy converter (WEC) that combines an oscillating surge wave energy converter with variable structural components. The control of the power-take-off torque will be on a wave-to-wave timescale, whereas the structure will be controlled statically such that the geometry remains the same throughout the wave period. Linear hydrodynamic theory is used to calculate the upper and lower bounds for the time-averaged absorbed power and surge foundation loads while assuming that the WEC motion remains sinusoidal. Previous work using pseudo-spectral techniques to solvemore » the optimal control problem focused solely on maximizing absorbed energy. This work extends the optimal control problem to include a measure of the surge foundation force in the optimization. The objective function includes two competing terms that force the optimizer to maximize power capture while minimizing structural loads. A penalty weight was included with the surge foundation force that allows control of the optimizer performance based on whether emphasis should be placed on power absorption or load shedding. Results from pseudo-spectral optimal control indicate that a unit reduction in time-averaged power can be accompanied by a greater reduction in surge-foundation force.« less

  14. Pseudo-spectral control of a novel oscillating surge wave energy converter in regular waves for power optimization including load reduction

    DOE PAGES

    Tom, Nathan M.; Yu, Yi -Hsiang; Wright, Alan D.; ...

    2017-04-18

    The aim of this study is to describe a procedure to maximize the power-to-load ratio of a novel wave energy converter (WEC) that combines an oscillating surge wave energy converter with variable structural components. The control of the power-take-off torque will be on a wave-to-wave timescale, whereas the structure will be controlled statically such that the geometry remains the same throughout the wave period. Linear hydrodynamic theory is used to calculate the upper and lower bounds for the time-averaged absorbed power and surge foundation loads while assuming that the WEC motion remains sinusoidal. Previous work using pseudo-spectral techniques to solvemore » the optimal control problem focused solely on maximizing absorbed energy. This work extends the optimal control problem to include a measure of the surge foundation force in the optimization. The objective function includes two competing terms that force the optimizer to maximize power capture while minimizing structural loads. A penalty weight was included with the surge foundation force that allows control of the optimizer performance based on whether emphasis should be placed on power absorption or load shedding. Results from pseudo-spectral optimal control indicate that a unit reduction in time-averaged power can be accompanied by a greater reduction in surge-foundation force.« less

  15. Aggregation Pheromone System: A Real-parameter Optimization Algorithm using Aggregation Pheromones as the Base Metaphor

    NASA Astrophysics Data System (ADS)

    Tsutsui, Shigeyosi

    This paper proposes an aggregation pheromone system (APS) for solving real-parameter optimization problems using the collective behavior of individuals which communicate using aggregation pheromones. APS was tested on several test functions used in evolutionary computation. The results showed APS could solve real-parameter optimization problems fairly well. The sensitivity analysis of control parameters of APS is also studied.

  16. An optimal control approach to the design of moving flight simulators

    NASA Technical Reports Server (NTRS)

    Sivan, R.; Ish-Shalom, J.; Huang, J.-K.

    1982-01-01

    An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

  17. A guidance law for hypersonic descent to a point

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

    Eisler, G.R.; Hull, D.G.

    1992-05-01

    A neighboring external control problem is formulated for a hypersonic glider to execute a maximum-terminal-velocity descent to a stationary target. The resulting two-part, feedback control scheme initially solves a nonlinear algebraic problem to generate a nominal trajectory to the target altitude. Secondly, a neighboring optimal path computation about the nominal provides a lift and side-force perturbations necessary to achieve the target downrange and crossrange. On-line feedback simulations of the proposed scheme and a form of proportional navigation are compared with an off-line parameter optimization method. The neighboring optimal terminal velocity compares very well with the parameter optimization solution and ismore » far superior to proportional navigation. 8 refs.« less

  18. A guidance law for hypersonic descent to a point

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

    Eisler, G.R.; Hull, D.G.

    1992-01-01

    A neighboring external control problem is formulated for a hypersonic glider to execute a maximum-terminal-velocity descent to a stationary target. The resulting two-part, feedback control scheme initially solves a nonlinear algebraic problem to generate a nominal trajectory to the target altitude. Secondly, a neighboring optimal path computation about the nominal provides a lift and side-force perturbations necessary to achieve the target downrange and crossrange. On-line feedback simulations of the proposed scheme and a form of proportional navigation are compared with an off-line parameter optimization method. The neighboring optimal terminal velocity compares very well with the parameter optimization solution and ismore » far superior to proportional navigation. 8 refs.« less

  19. Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

    PubMed Central

    Zatsiorsky, Vladimir M.

    2011-01-01

    One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

  20. 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.

  1. Rapid Preliminary Design of Interplanetary Trajectories Using the Evolutionary Mission Trajectory Generator

    NASA Technical Reports Server (NTRS)

    Englander, Jacob

    2016-01-01

    Preliminary design of interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on notional high-thrust chemical and low-thrust electric propulsion missions. In the low-thrust case, the hybrid optimal control problem is augmented to include systems design optimization.

  2. An optimal control strategy for collision avoidance of mobile robots in non-stationary environments

    NASA Technical Reports Server (NTRS)

    Kyriakopoulos, K. J.; Saridis, G. N.

    1991-01-01

    An optimal control formulation of the problem of collision avoidance of mobile robots in environments containing moving obstacles is presented. Collision avoidance is guaranteed if the minimum distance between the robot and the objects is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Furthermore, time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. Simulation results verify the value of the proposed strategy.

  3. Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

    Ma, Xiao; Dong, Jin; Djouadi, Seddik M

    2015-01-01

    The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

  4. Attitude guidance and tracking for spacecraft with two reaction wheels

    NASA Astrophysics Data System (ADS)

    Biggs, James D.; Bai, Yuliang; Henninger, Helen

    2018-04-01

    This paper addresses the guidance and tracking problem for a rigid-spacecraft using two reaction wheels (RWs). The guidance problem is formulated as an optimal control problem on the special orthogonal group SO(3). The optimal motion is solved analytically as a function of time and is used to reduce the original guidance problem to one of computing the minimum of a nonlinear function. A tracking control using two RWs is developed that extends previous singular quaternion stabilisation controls to tracking controls on the rotation group. The controller is proved to locally asymptotically track the generated reference motions using Lyapunov's direct method. Simulations of a 3U CubeSat demonstrate that this tracking control is robust to initial rotation errors and angular velocity errors in the controlled axis. For initial angular velocity errors in the uncontrolled axis and under significant disturbances the control fails to track. However, the singular tracking control is combined with a nano-magnetic torquer which simply damps the angular velocity in the uncontrolled axis and is shown to provide a practical control method for tracking in the presence of disturbances and initial condition errors.

  5. Statistical estimation via convex optimization for trending and performance monitoring

    NASA Astrophysics Data System (ADS)

    Samar, Sikandar

    This thesis presents an optimization-based statistical estimation approach to find unknown trends in noisy data. A Bayesian framework is used to explicitly take into account prior information about the trends via trend models and constraints. The main focus is on convex formulation of the Bayesian estimation problem, which allows efficient computation of (globally) optimal estimates. There are two main parts of this thesis. The first part formulates trend estimation in systems described by known detailed models as a convex optimization problem. Statistically optimal estimates are then obtained by maximizing a concave log-likelihood function subject to convex constraints. We consider the problem of increasing problem dimension as more measurements become available, and introduce a moving horizon framework to enable recursive estimation of the unknown trend by solving a fixed size convex optimization problem at each horizon. We also present a distributed estimation framework, based on the dual decomposition method, for a system formed by a network of complex sensors with local (convex) estimation. Two specific applications of the convex optimization-based Bayesian estimation approach are described in the second part of the thesis. Batch estimation for parametric diagnostics in a flight control simulation of a space launch vehicle is shown to detect incipient fault trends despite the natural masking properties of feedback in the guidance and control loops. Moving horizon approach is used to estimate time varying fault parameters in a detailed nonlinear simulation model of an unmanned aerial vehicle. An excellent performance is demonstrated in the presence of winds and turbulence.

  6. Cartesian control of redundant robots

    NASA Technical Reports Server (NTRS)

    Colbaugh, R.; Glass, K.

    1989-01-01

    A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.

  7. 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.

  8. Blended near-optimal alternative generation, visualization, and interaction for water resources decision making

    NASA Astrophysics Data System (ADS)

    Rosenberg, David E.

    2015-04-01

    State-of-the-art systems analysis techniques focus on efficiently finding optimal solutions. Yet an optimal solution is optimal only for the modeled issues and managers often seek near-optimal alternatives that address unmodeled objectives, preferences, limits, uncertainties, and other issues. Early on, Modeling to Generate Alternatives (MGA) formalized near-optimal as performance within a tolerable deviation from the optimal objective function value and identified a few maximally different alternatives that addressed some unmodeled issues. This paper presents new stratified, Monte-Carlo Markov Chain sampling and parallel coordinate plotting tools that generate and communicate the structure and extent of the near-optimal region to an optimization problem. Interactive plot controls allow users to explore region features of most interest. Controls also streamline the process to elicit unmodeled issues and update the model formulation in response to elicited issues. Use for an example, single-objective, linear water quality management problem at Echo Reservoir, Utah, identifies numerous and flexible practices to reduce the phosphorus load to the reservoir and maintain close-to-optimal performance. Flexibility is upheld by further interactive alternative generation, transforming the formulation into a multiobjective problem, and relaxing the tolerance parameter to expand the near-optimal region. Compared to MGA, the new blended tools generate more numerous alternatives faster, more fully show the near-optimal region, and help elicit a larger set of unmodeled issues.

  9. Hodograph analysis in aircraft trajectory optimization

    NASA Technical Reports Server (NTRS)

    Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.

    1993-01-01

    An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

  10. Optimal Control of Thermo--Fluid Phenomena in Variable Domains

    NASA Astrophysics Data System (ADS)

    Volkov, Oleg; Protas, Bartosz

    2008-11-01

    This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an illustration we will consider the two--phase Stefan problem with contact point singularities where our approach allows us to obtain a thermodynamically consistent solution.

  11. Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

    NASA Technical Reports Server (NTRS)

    Liu, Gao-Lian

    1991-01-01

    Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

  12. Consideration of computer limitations in implementing on-line controls. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Roberts, G. K.

    1976-01-01

    A formal statement of the optimal control problem which includes the interval of dicretization as an optimization parameter, and extend this to include selection of a control algorithm as part of the optimization procedure, is formulated. The performance of the scalar linear system depends on the discretization interval. Discrete-time versions of the output feedback regulator and an optimal compensator, and the use of these results in presenting an example of a system for which fast partial-state-feedback control better minimizes a quadratic cost than either a full-state feedback control or a compensator, are developed.

  13. 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.

  14. Optimal Control via Self-Generated Stochasticity

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2011-01-01

    The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

  15. Dynamic optimization and its relation to classical and quantum constrained systems

    NASA Astrophysics Data System (ADS)

    Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

    2017-08-01

    We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

  16. On actuator placement for robust time-optimal control of uncertain flexible spacecraft

    NASA Technical Reports Server (NTRS)

    Wie, Bong; Sinha, Ravi; Liu, Qiang

    1992-01-01

    The problem of computing open-loop, on-off jet firing logic for flexible spacecraft in the face of plant modeling uncertainty is investigated. The primary control objective is to achieve a fast maneuvering time with a minimum of structural vibrations during and/or after a maneuver. This paper is also concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated. A three-mass-spring model of flexible spacecraft with a rigid-body mode and two flexible modes is used to illustrate the concept.

  17. Necessary optimality conditions for infinite dimensional state constrained control problems

    NASA Astrophysics Data System (ADS)

    Frankowska, H.; Marchini, E. M.; Mazzola, M.

    2018-06-01

    This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.

  18. 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.

  19. On stochastic control and optimal measurement strategies. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Kramer, L. C.

    1971-01-01

    The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

  20. Modeling of tool path for the CNC sheet cutting machines

    NASA Astrophysics Data System (ADS)

    Petunin, Aleksandr A.

    2015-11-01

    In the paper the problem of tool path optimization for CNC (Computer Numerical Control) cutting machines is considered. The classification of the cutting techniques is offered. We also propose a new classification of toll path problems. The tasks of cost minimization and time minimization for standard cutting technique (Continuous Cutting Problem, CCP) and for one of non-standard cutting techniques (Segment Continuous Cutting Problem, SCCP) are formalized. We show that the optimization tasks can be interpreted as discrete optimization problem (generalized travel salesman problem with additional constraints, GTSP). Formalization of some constraints for these tasks is described. For the solution GTSP we offer to use mathematical model of Prof. Chentsov based on concept of a megalopolis and dynamic programming.

  1. Genetic-evolution-based optimization methods for engineering design

    NASA Technical Reports Server (NTRS)

    Rao, S. S.; Pan, T. S.; Dhingra, A. K.; Venkayya, V. B.; Kumar, V.

    1990-01-01

    This paper presents the applicability of a biological model, based on genetic evolution, for engineering design optimization. Algorithms embodying the ideas of reproduction, crossover, and mutation are developed and applied to solve different types of structural optimization problems. Both continuous and discrete variable optimization problems are solved. A two-bay truss for maximum fundamental frequency is considered to demonstrate the continuous variable case. The selection of locations of actuators in an actively controlled structure, for minimum energy dissipation, is considered to illustrate the discrete variable case.

  2. Optimizing the sequence of diameter distributions and selection harvests for uneven-aged stand management

    Treesearch

    Robert G. Haight; J. Douglas Brodie; Darius M. Adams

    1985-01-01

    The determination of an optimal sequence of diameter distributions and selection harvests for uneven-aged stand management is formulated as a discrete-time optimal-control problem with bounded control variables and free-terminal point. An efficient programming technique utilizing gradients provides solutions that are stable and interpretable on the basis of economic...

  3. Synthesis of multi-loop automatic control systems by the nonlinear programming method

    NASA Astrophysics Data System (ADS)

    Voronin, A. V.; Emelyanova, T. A.

    2017-01-01

    The article deals with the problem of calculation of the multi-loop control systems optimal tuning parameters by numerical methods and nonlinear programming methods. For this purpose, in the paper the Optimization Toolbox of Matlab is used.

  4. Optimal ballistically captured Earth-Moon transfers

    NASA Astrophysics Data System (ADS)

    Ricord Griesemer, Paul; Ocampo, Cesar; Cooley, D. S.

    2012-07-01

    The optimality of a low-energy Earth-Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth-Moon ballistic lunar capture transfers.

  5. Analysis Balance Parameter of Optimal Ramp metering

    NASA Astrophysics Data System (ADS)

    Li, Y.; Duan, N.; Yang, X.

    2018-05-01

    Ramp metering is a motorway control method to avoid onset congestion through limiting the access of ramp inflows into the main road of the motorway. The optimization model of ramp metering is developed based upon cell transmission model (CTM). With the piecewise linear structure of CTM, the corresponding motorway traffic optimization problem can be formulated as a linear programming (LP) problem. It is known that LP problem can be solved by established solution algorithms such as SIMPLEX or interior-point methods for the global optimal solution. The commercial software (CPLEX) is adopted in this study to solve the LP problem within reasonable computational time. The concept is illustrated through a case study of the United Kingdom M25 Motorway. The optimal solution provides useful insights and guidances on how to manage motorway traffic in order to maximize the corresponding efficiency.

  6. Linear quadratic optimization for positive LTI system

    NASA Astrophysics Data System (ADS)

    Muhafzan, Yenti, Syafrida Wirma; Zulakmal

    2017-05-01

    Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

  7. 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.

  8. Automatic weight determination in nonlinear model predictive control of wind turbines using swarm optimization technique

    NASA Astrophysics Data System (ADS)

    Tofighi, Elham; Mahdizadeh, Amin

    2016-09-01

    This paper addresses the problem of automatic tuning of weighting coefficients for the nonlinear model predictive control (NMPC) of wind turbines. The choice of weighting coefficients in NMPC is critical due to their explicit impact on efficiency of the wind turbine control. Classically, these weights are selected based on intuitive understanding of the system dynamics and control objectives. The empirical methods, however, may not yield optimal solutions especially when the number of parameters to be tuned and the nonlinearity of the system increase. In this paper, the problem of determining weighting coefficients for the cost function of the NMPC controller is formulated as a two-level optimization process in which the upper- level PSO-based optimization computes the weighting coefficients for the lower-level NMPC controller which generates control signals for the wind turbine. The proposed method is implemented to tune the weighting coefficients of a NMPC controller which drives the NREL 5-MW wind turbine. The results are compared with similar simulations for a manually tuned NMPC controller. Comparison verify the improved performance of the controller for weights computed with the PSO-based technique.

  9. Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

    NASA Astrophysics Data System (ADS)

    Sutrisno, Widowati, Tjahjana, R. Heru

    2017-12-01

    The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

  10. Receding horizon online optimization for torque control of gasoline engines.

    PubMed

    Kang, Mingxin; Shen, Tielong

    2016-11-01

    This paper proposes a model-based nonlinear receding horizon optimal control scheme for the engine torque tracking problem. The controller design directly employs the nonlinear model exploited based on mean-value modeling principle of engine systems without any linearizing reformation, and the online optimization is achieved by applying the Continuation/GMRES (generalized minimum residual) approach. Several receding horizon control schemes are designed to investigate the effects of the integral action and integral gain selection. Simulation analyses and experimental validations are implemented to demonstrate the real-time optimization performance and control effects of the proposed torque tracking controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

    NASA Technical Reports Server (NTRS)

    Hull, P. V.; Tinker, M. L.

    2007-01-01

    Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

  12. 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.

  13. 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.

  14. 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.

  15. Optimisation of strain selection in evolutionary continuous culture

    NASA Astrophysics Data System (ADS)

    Bayen, T.; Mairet, F.

    2017-12-01

    In this work, we study a minimal time control problem for a perfectly mixed continuous culture with n ≥ 2 species and one limiting resource. The model that we consider includes a mutation factor for the microorganisms. Our aim is to provide optimal feedback control laws to optimise the selection of the species of interest. Thanks to Pontryagin's Principle, we derive optimality conditions on optimal controls and introduce a sub-optimal control law based on a most rapid approach to a singular arc that depends on the initial condition. Using adaptive dynamics theory, we also study a simplified version of this model which allows to introduce a near optimal strategy.

  16. Optimizing Dynamical Network Structure for Pinning Control

    NASA Astrophysics Data System (ADS)

    Orouskhani, Yasin; Jalili, Mahdi; Yu, Xinghuo

    2016-04-01

    Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.

  17. 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.

  18. Real-Time Load-Side Control of Electric Power Systems

    NASA Astrophysics Data System (ADS)

    Zhao, Changhong

    Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems. (1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control. (2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.

  19. Distributed Method to Optimal Profile Descent

    NASA Astrophysics Data System (ADS)

    Kim, Geun I.

    Current ground automation tools for Optimal Profile Descent (OPD) procedures utilize path stretching and speed profile change to maintain proper merging and spacing requirements at high traffic terminal area. However, low predictability of aircraft's vertical profile and path deviation during decent add uncertainty to computing estimated time of arrival, a key information that enables the ground control center to manage airspace traffic effectively. This paper uses an OPD procedure that is based on a constant flight path angle to increase the predictability of the vertical profile and defines an OPD optimization problem that uses both path stretching and speed profile change while largely maintaining the original OPD procedure. This problem minimizes the cumulative cost of performing OPD procedures for a group of aircraft by assigning a time cost function to each aircraft and a separation cost function to a pair of aircraft. The OPD optimization problem is then solved in a decentralized manner using dual decomposition techniques under inter-aircraft ADS-B mechanism. This method divides the optimization problem into more manageable sub-problems which are then distributed to the group of aircraft. Each aircraft solves its assigned sub-problem and communicate the solutions to other aircraft in an iterative process until an optimal solution is achieved thus decentralizing the computation of the optimization problem.

  20. Optimal control of switching time in switched stochastic systems with multi-switching times and different costs

    NASA Astrophysics Data System (ADS)

    Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian

    2017-08-01

    In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.

  1. Affective personality as cognitive-emotional presymptom profiles regulatory for self-reported health predispositions.

    PubMed

    Archer, T; Adolfsson, B; Karlsson, E

    2008-08-01

    Three studies that examined the links between affective personality, as constructed from responses to the Positive Affect (PA) and Negative Affect (NA) Scale (PANAS), and individuals' self-report of self-esteem, intrinsic motivation and Beck's Depression Inventory (BDI) depression in high school students and persons in working occupations are described. Self-report estimations of several other neuropsychiatric and psychosocial variables including, the Uppsala Sleep Inventory (USI), the Hospital Anxiety and Depression (HAD) test, Dispositional optimism, Locus of control, the Subjective Stress Experience test (SSE) and the Stress-Energy (SE) test, were also derived. Marked effects due to affective personality type upon somatic and psychological stress, anxiety and depression, self-esteem, internal and external locus of control, optimism, stress and energy, intrinsic motivation, external regulation, identified regulation, major sleep problems, problems falling asleep, and psychophysiological problems were observed; levels of self-esteem, self-motivation and BDI-depression all produced substantial effects on health and well-being. Regression analyses indicated PA was predicted by dispositional optimism (thrice), energy (thrice), and intrinsic motivation, and counter predicted by depression (twice) and stress (twice); and NA by anxiety (twice), stress (twice), psychological stress, identified regulation, BDI depression and psychophysiological problems, and counter predicted by internal locus of control and self-esteem. BDI-depression was predicted by negative affect, major sleep problems and psychophysiological problems (Study III), self-esteem by dispositional optimism and energy, and counter predicted by anxiety, depression and stress (Study I), and intrinsic motivation by dispositional optimism, energy, PA and self-esteem (Study II). These convergent findings are interpreted from a perspective of the cognitive-emotional expressions underlying behavioural or presymptomatic profiles presenting predispositions for health or ill health.

  2. Optimization-based power management of hybrid power systems with applications in advanced hybrid electric vehicles and wind farms with battery storage

    NASA Astrophysics Data System (ADS)

    Borhan, Hoseinali

    Modern hybrid electric vehicles and many stationary renewable power generation systems combine multiple power generating and energy storage devices to achieve an overall system-level efficiency and flexibility which is higher than their individual components. The power or energy management control, "brain" of these "hybrid" systems, determines adaptively and based on the power demand the power split between multiple subsystems and plays a critical role in overall system-level efficiency. This dissertation proposes that a receding horizon optimal control (aka Model Predictive Control) approach can be a natural and systematic framework for formulating this type of power management controls. More importantly the dissertation develops new results based on the classical theory of optimal control that allow solving the resulting optimal control problem in real-time, in spite of the complexities that arise due to several system nonlinearities and constraints. The dissertation focus is on two classes of hybrid systems: hybrid electric vehicles in the first part and wind farms with battery storage in the second part. The first part of the dissertation proposes and fully develops a real-time optimization-based power management strategy for hybrid electric vehicles. Current industry practice uses rule-based control techniques with "else-then-if" logic and look-up maps and tables in the power management of production hybrid vehicles. These algorithms are not guaranteed to result in the best possible fuel economy and there exists a gap between their performance and a minimum possible fuel economy benchmark. Furthermore, considerable time and effort are spent calibrating the control system in the vehicle development phase, and there is little flexibility in real-time handling of constraints and re-optimization of the system operation in the event of changing operating conditions and varying parameters. In addition, a proliferation of different powertrain configurations may result in the need for repeated control system redesign. To address these shortcomings, we formulate the power management problem as a nonlinear and constrained optimal control problem. Solution of this optimal control problem in real-time on chronometric- and memory-constrained automotive microcontrollers is quite challenging; this computational complexity is due to the highly nonlinear dynamics of the powertrain subsystems, mixed-integer switching modes of their operation, and time-varying and nonlinear hard constraints that system variables should satisfy. The main contribution of the first part of the dissertation is that it establishes methods for systematic and step-by step improvements in fuel economy while maintaining the algorithmic computational requirements in a real-time implementable framework. More specifically a linear time-varying model predictive control approach is employed first which uses sequential quadratic programming to find sub-optimal solutions to the power management problem. Next the objective function is further refined and broken into a short and a long horizon segments; the latter approximated as a function of the state using the connection between the Pontryagin minimum principle and Hamilton-Jacobi-Bellman equations. The power management problem is then solved using a nonlinear MPC framework with a dynamic programming solver and the fuel economy is further improved. Typical simplifying academic assumptions are minimal throughout this work, thanks to close collaboration with research scientists at Ford research labs and their stringent requirement that the proposed solutions be tested on high-fidelity production models. Simulation results on a high-fidelity model of a hybrid electric vehicle over multiple standard driving cycles reveal the potential for substantial fuel economy gains. To address the control calibration challenges, we also present a novel and fast calibration technique utilizing parallel computing techniques. ^ The second part of this dissertation presents an optimization-based control strategy for the power management of a wind farm with battery storage. The strategy seeks to minimize the error between the power delivered by the wind farm with battery storage and the power demand from an operator. In addition, the strategy attempts to maximize battery life. The control strategy has two main stages. The first stage produces a family of control solutions that minimize the power error subject to the battery constraints over an optimization horizon. These solutions are parameterized by a given value for the state of charge at the end of the optimization horizon. The second stage screens the family of control solutions to select one attaining an optimal balance between power error and battery life. The battery life model used in this stage is a weighted Amp-hour (Ah) throughput model. The control strategy is modular, allowing for more sophisticated optimization models in the first stage, or more elaborate battery life models in the second stage. The strategy is implemented in real-time in the framework of Model Predictive Control (MPC).

  3. Intelligent and robust optimization frameworks for smart grids

    NASA Astrophysics Data System (ADS)

    Dhansri, Naren Reddy

    A smart grid implies a cyberspace real-time distributed power control system to optimally deliver electricity based on varying consumer characteristics. Although smart grids solve many of the contemporary problems, they give rise to new control and optimization problems with the growing role of renewable energy sources such as wind or solar energy. Under highly dynamic nature of distributed power generation and the varying consumer demand and cost requirements, the total power output of the grid should be controlled such that the load demand is met by giving a higher priority to renewable energy sources. Hence, the power generated from renewable energy sources should be optimized while minimizing the generation from non renewable energy sources. This research develops a demand-based automatic generation control and optimization framework for real-time smart grid operations by integrating conventional and renewable energy sources under varying consumer demand and cost requirements. Focusing on the renewable energy sources, the intelligent and robust control frameworks optimize the power generation by tracking the consumer demand in a closed-loop control framework, yielding superior economic and ecological benefits and circumvent nonlinear model complexities and handles uncertainties for superior real-time operations. The proposed intelligent system framework optimizes the smart grid power generation for maximum economical and ecological benefits under an uncertain renewable wind energy source. The numerical results demonstrate that the proposed framework is a viable approach to integrate various energy sources for real-time smart grid implementations. The robust optimization framework results demonstrate the effectiveness of the robust controllers under bounded power plant model uncertainties and exogenous wind input excitation while maximizing economical and ecological performance objectives. Therefore, the proposed framework offers a new worst-case deterministic optimization algorithm for smart grid automatic generation control.

  4. Optimal motion planning for collision avoidance of mobile robots in non-stationary environments

    NASA Technical Reports Server (NTRS)

    Kyriakopoulos, K. J.; Saridis, G. N.

    1992-01-01

    An optimal control formulation of the problem of collision avoidance of mobile robots moving in general terrains containing moving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the minimum distance between the robot and the object is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. A perturbation control type of approach is used to update the optimal plan. Simulation results verify the value of the proposed strategy.

  5. CONSOLE: A CAD tandem for optimization-based design interacting with user-supplied simulators

    NASA Technical Reports Server (NTRS)

    Fan, Michael K. H.; Wang, Li-Sheng; Koninckx, Jan; Tits, Andre L.

    1989-01-01

    CONSOLE employs a recently developed design methodology (International Journal of Control 43:1693-1721) which provides the designer with a congenial environment to express his problem as a multiple ojective constrained optimization problem and allows him to refine his characterization of optimality when a suboptimal design is approached. To this end, in CONSOLE, the designed formulates the design problem using a high-level language and performs design task and explores tradeoff through a few short and clearly defined commands. The range of problems that can be solved efficiently using a CAD tools depends very much on the ability of this tool to be interfaced with user-supplied simulators. For instance, when designing a control system one makes use of the characteristics of the plant, and therefore, a model of the plant under study has to be made available to the CAD tool. CONSOLE allows for an easy interfacing of almost any simulator the user has available. To date CONSOLE has already been used successfully in many applications, including the design of controllers for a flexible arm and for a robotic manipulator and the solution of a parameter selection problem for a neural network.

  6. Optimal spacecraft attitude control using collocation and nonlinear programming

    NASA Astrophysics Data System (ADS)

    Herman, A. L.; Conway, B. A.

    1992-10-01

    Direct collocation with nonlinear programming (DCNLP) is employed to find the optimal open-loop control histories for detumbling a disabled satellite. The controls are torques and forces applied to the docking arm and joint and torques applied about the body axes of the OMV. Solutions are obtained for cases in which various constraints are placed on the controls and in which the number of controls is reduced or increased from that considered in Conway and Widhalm (1986). DCLNP works well when applied to the optimal control problem of satellite attitude control. The formulation is straightforward and produces good results in a relatively small amount of time on a Cray X/MP with no a priori information about the optimal solution. The addition of joint acceleration to the controls significantly reduces the control magnitudes and optimal cost. In all cases, the torques and acclerations are modest and the optimal cost is very modest.

  7. Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.

    NASA Astrophysics Data System (ADS)

    Velichkin, Vladimir A.; Zavyalov, Vladimir A.

    2018-03-01

    This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.

  8. Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

    NASA Technical Reports Server (NTRS)

    Balakrishnan, A. V.

    1994-01-01

    This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

  9. Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

    NASA Technical Reports Server (NTRS)

    Balakrishnan, A. V.

    1994-01-01

    This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

  10. Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

    NASA Astrophysics Data System (ADS)

    Han, Jiang; Chen, Ye-Hwa; Zhao, Xiaomin; Dong, Fangfang

    2018-04-01

    A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.

  11. Optimal control on bladder cancer growth model with BCG immunotherapy and chemotherapy

    NASA Astrophysics Data System (ADS)

    Dewi, C.; Trisilowati

    2015-03-01

    In this paper, an optimal control model of the growth of bladder cancer with BCG (Basil Calmate Guerin) immunotherapy and chemotherapy is discussed. The purpose of this optimal control is to determine the number of BCG vaccine and drug should be given during treatment such that the growth of bladder cancer cells can be suppressed. Optimal control is obtained by applying Pontryagin principle. Furthermore, the optimal control problem is solved numerically using Forward-Backward Sweep method. Numerical simulations show the effectiveness of the vaccine and drug in controlling the growth of cancer cells. Hence, it can reduce the number of cancer cells that is not infected with BCG as well as minimize the cost of the treatment.

  12. Solving the optimal attention allocation problem in manual control

    NASA Technical Reports Server (NTRS)

    Kleinman, D. L.

    1976-01-01

    Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.

  13. Differential geometric methods in system theory.

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.

    1971-01-01

    Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

  14. A genetic technique for planning a control sequence to navigate the state space with a quasi-minimum-cost output trajectory for a non-linear multi-dimnensional system

    NASA Technical Reports Server (NTRS)

    Hein, C.; Meystel, A.

    1994-01-01

    There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.

  15. Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

    PubMed

    Liu, Meiqin

    2009-09-01

    This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

  16. A method to stabilize linear systems using eigenvalue gradient information

    NASA Technical Reports Server (NTRS)

    Wieseman, C. D.

    1985-01-01

    Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

  17. Everyday Experiences of Memory Problems and Control: The Adaptive Role of Selective Optimization with Compensation in the Context of Memory Decline

    PubMed Central

    Hahn, Elizabeth A.; Lachman, Margie E.

    2014-01-01

    The present study examined the role of long-term working memory decline in the relationship between everyday experiences of memory problems and perceived control, and we also considered whether the use of accommodative strategies [selective optimization with compensation (SOC)] would be adaptive. The study included Boston-area participants (n=103) from the Midlife in the United States study (MIDUS) who completed two working memory assessments over ten years and weekly diaries following Time 2. In adjusted multi-level analyses, greater memory decline and lower general perceived control were associated with more everyday memory problems. Low perceived control reported in a weekly diary was associated with more everyday memory problems among those with greater memory decline and low SOC strategy use (Est.=−0.28, SE=0.13, p=.036). These results suggest that the use of SOC strategies in the context of declining memory may help to buffer the negative effects of low perceived control on everyday memory. PMID:24597768

  18. Making the EZ Choice

    NASA Technical Reports Server (NTRS)

    2001-01-01

    Analytical Mechanics Associates, Inc. (AMA), of Hampton, Virginia, created the EZopt software application through Small Business Innovation Research (SBIR) funding from NASA's Langley Research Center. The new software is a user-friendly tool kit that provides quick and logical solutions to complex optimal control problems. In its most basic form, EZopt converts process data into math equations and then proceeds to utilize those equations to solve problems within control systems. EZopt successfully proved its advantage when applied to short-term mission planning and onboard flight computer implementation. The technology has also solved multiple real-life engineering problems faced in numerous commercial operations. For instance, mechanical engineers use EZopt to solve control problems with robots, while chemical plants implement the application to overcome situations with batch reactors and temperature control. In the emerging field of commercial aerospace, EZopt is able to optimize trajectories for launch vehicles and perform potential space station- keeping tasks. Furthermore, the software also helps control electromagnetic devices in the automotive industry.

  19. 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.

  20. Everyday experiences of memory problems and control: the adaptive role of selective optimization with compensation in the context of memory decline.

    PubMed

    Hahn, Elizabeth A; Lachman, Margie E

    2015-01-01

    The present study examined the role of long-term working memory decline in the relationship between everyday experiences of memory problems and perceived control, and we also considered whether the use of accommodative strategies [selective optimization with compensation (SOC)] would be adaptive. The study included Boston-area participants (n = 103) from the Midlife in the United States study (MIDUS) who completed two working memory assessments over 10 years and weekly diaries following Time 2. In adjusted multi-level analyses, greater memory decline and lower general perceived control were associated with more everyday memory problems. Low perceived control reported in a weekly diary was associated with more everyday memory problems among those with greater memory decline and low SOC strategy use (Est. = -0.28, SE= 0.13, p = .036). These results suggest that the use of SOC strategies in the context of declining memory may help to buffer the negative effects of low perceived control on everyday memory.

  1. Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

    NASA Astrophysics Data System (ADS)

    Krasovskii, A. A.; Lebedev, P. D.; Tarasyev, A. M.

    2017-05-01

    We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.

  2. Active model-based balancing strategy for self-reconfigurable batteries

    NASA Astrophysics Data System (ADS)

    Bouchhima, Nejmeddine; Schnierle, Marc; Schulte, Sascha; Birke, Kai Peter

    2016-08-01

    This paper describes a novel balancing strategy for self-reconfigurable batteries where the discharge and charge rates of each cell can be controlled. While much effort has been focused on improving the hardware architecture of self-reconfigurable batteries, energy equalization algorithms have not been systematically optimized in terms of maximizing the efficiency of the balancing system. Our approach includes aspects of such optimization theory. We develop a balancing strategy for optimal control of the discharge rate of battery cells. We first formulate the cell balancing as a nonlinear optimal control problem, which is modeled afterward as a network program. Using dynamic programming techniques and MATLAB's vectorization feature, we solve the optimal control problem by generating the optimal battery operation policy for a given drive cycle. The simulation results show that the proposed strategy efficiently balances the cells over the life of the battery, an obvious advantage that is absent in the other conventional approaches. Our algorithm is shown to be robust when tested against different influencing parameters varying over wide spectrum on different drive cycles. Furthermore, due to the little computation time and the proved low sensitivity to the inaccurate power predictions, our strategy can be integrated in a real-time system.

  3. Application of modern control theory to scheduling and path-stretching maneuvers of aircraft in the near terminal area

    NASA Technical Reports Server (NTRS)

    Athans, M.

    1974-01-01

    A design concept of the dynamic control of aircraft in the near terminal area is discussed. An arbitrary set of nominal air routes, with possible multiple merging points, all leading to a single runway, is considered. The system allows for the automated determination of acceleration/deceleration of aircraft along the nominal air routes, as well as for the automated determination of path-stretching delay maneuvers. In addition to normal operating conditions, the system accommodates: (1) variable commanded separations over the outer marker to allow for takeoffs and between successive landings and (2) emergency conditions under which aircraft in distress have priority. The system design is based on a combination of three distinct optimal control problems involving a standard linear-quadratic problem, a parameter optimization problem, and a minimum-time rendezvous problem.

  4. Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model

    NASA Astrophysics Data System (ADS)

    Wiezel, Oren; Or, Yizhar

    2016-11-01

    Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.

  5. Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

    NASA Astrophysics Data System (ADS)

    Sobolic, Frantisek M.

    Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.

  6. Control and structural optimization for maneuvering large spacecraft

    NASA Technical Reports Server (NTRS)

    Chun, H. M.; Turner, J. D.; Yu, C. C.

    1990-01-01

    Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment.

  7. Optimized Assistive Human-Robot Interaction Using Reinforcement Learning.

    PubMed

    Modares, Hamidreza; Ranatunga, Isura; Lewis, Frank L; Popa, Dan O

    2016-03-01

    An intelligent human-robot interaction (HRI) system with adjustable robot behavior is presented. The proposed HRI system assists the human operator to perform a given task with minimum workload demands and optimizes the overall human-robot system performance. Motivated by human factor studies, the presented control structure consists of two control loops. First, a robot-specific neuro-adaptive controller is designed in the inner loop to make the unknown nonlinear robot behave like a prescribed robot impedance model as perceived by a human operator. In contrast to existing neural network and adaptive impedance-based control methods, no information of the task performance or the prescribed robot impedance model parameters is required in the inner loop. Then, a task-specific outer-loop controller is designed to find the optimal parameters of the prescribed robot impedance model to adjust the robot's dynamics to the operator skills and minimize the tracking error. The outer loop includes the human operator, the robot, and the task performance details. The problem of finding the optimal parameters of the prescribed robot impedance model is transformed into a linear quadratic regulator (LQR) problem which minimizes the human effort and optimizes the closed-loop behavior of the HRI system for a given task. To obviate the requirement of the knowledge of the human model, integral reinforcement learning is used to solve the given LQR problem. Simulation results on an x - y table and a robot arm, and experimental implementation results on a PR2 robot confirm the suitability of the proposed method.

  8. 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.

  9. Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

    NASA Technical Reports Server (NTRS)

    Burns, John A.; Marrekchi, Hamadi

    1993-01-01

    The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

  10. 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.

  11. Real-Time Control of an Ensemble of Heterogeneous Resources

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

    Bernstein, Andrey; Bouman, Niek J.; Le Boudec, Jean-Yves

    This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimizationmore » problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.« less

  12. A single sensor and single actuator approach to performance tailoring over a prescribed frequency band.

    PubMed

    Wang, Jiqiang

    2016-03-01

    Restricted sensing and actuation control represents an important area of research that has been overlooked in most of the design methodologies. In many practical control engineering problems, it is necessitated to implement the design through a single sensor and single actuator for multivariate performance variables. In this paper, a novel approach is proposed for the solution to the single sensor and single actuator control problem where performance over any prescribed frequency band can also be tailored. The results are obtained for the broad band control design based on the formulation for discrete frequency control. It is shown that the single sensor and single actuator control problem over a frequency band can be cast into a Nevanlinna-Pick interpolation problem. An optimal controller can then be obtained via the convex optimization over LMIs. Even remarkable is that robustness issues can also be tackled in this framework. A numerical example is provided for the broad band attenuation of rotor blade vibration to illustrate the proposed design procedures. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  13. A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles

    DOE PAGES

    Malikopoulos, Andreas

    2015-01-01

    The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.more » Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.« less

  14. A Coral Reef Algorithm Based on Learning Automata for the Coverage Control Problem of Heterogeneous Directional Sensor Networks

    PubMed Central

    Li, Ming; Miao, Chunyan; Leung, Cyril

    2015-01-01

    Coverage control is one of the most fundamental issues in directional sensor networks. In this paper, the coverage optimization problem in a directional sensor network is formulated as a multi-objective optimization problem. It takes into account the coverage rate of the network, the number of working sensor nodes and the connectivity of the network. The coverage problem considered in this paper is characterized by the geographical irregularity of the sensed events and heterogeneity of the sensor nodes in terms of sensing radius, field of angle and communication radius. To solve this multi-objective problem, we introduce a learning automata-based coral reef algorithm for adaptive parameter selection and use a novel Tchebycheff decomposition method to decompose the multi-objective problem into a single-objective problem. Simulation results show the consistent superiority of the proposed algorithm over alternative approaches. PMID:26690162

  15. A Coral Reef Algorithm Based on Learning Automata for the Coverage Control Problem of Heterogeneous Directional Sensor Networks.

    PubMed

    Li, Ming; Miao, Chunyan; Leung, Cyril

    2015-12-04

    Coverage control is one of the most fundamental issues in directional sensor networks. In this paper, the coverage optimization problem in a directional sensor network is formulated as a multi-objective optimization problem. It takes into account the coverage rate of the network, the number of working sensor nodes and the connectivity of the network. The coverage problem considered in this paper is characterized by the geographical irregularity of the sensed events and heterogeneity of the sensor nodes in terms of sensing radius, field of angle and communication radius. To solve this multi-objective problem, we introduce a learning automata-based coral reef algorithm for adaptive parameter selection and use a novel Tchebycheff decomposition method to decompose the multi-objective problem into a single-objective problem. Simulation results show the consistent superiority of the proposed algorithm over alternative approaches.

  16. The Riccati equation, imprimitive actions and symplectic forms. [with application to decentralized optimal control problem

    NASA Technical Reports Server (NTRS)

    Garzia, M. R.; Loparo, K. A.; Martin, C. F.

    1982-01-01

    This paper looks at the structure of the solution of a matrix Riccati differential equation under a predefined group of transformations. The group of transformations used is an expanded form of the feedback group. It is shown that this group of transformations is a subgroup of the symplectic group. The orbits of the Riccati differential equation under the action of this group are studied and it is seen how these techniques apply to a decentralized optimal control problem.

  17. Optimal control of lift/drag ratios on a rotating cylinder

    NASA Technical Reports Server (NTRS)

    Ou, Yuh-Roung; Burns, John A.

    1992-01-01

    We present the numerical solution to a problem of maximizing the lift to drag ratio by rotating a circular cylinder in a two-dimensional viscous incompressible flow. This problem is viewed as a test case for the newly developing theoretical and computational methods for control of fluid dynamic systems. We show that the time averaged lift to drag ratio for a fixed finite-time interval achieves its maximum value at an optimal rotation rate that depends on the time interval.

  18. Control of vibrations of a moving beam

    NASA Astrophysics Data System (ADS)

    Banichuk, N. V.; Ivanova, S. Yu; Makeev, E. V.; Sinitsyn, A. V.

    2018-04-01

    The translational motion of a thermoelastic beam under transverse vibrations caused by initial perturbations is considered. It is assumed that a beam moving at a constant translational speed is described by a model of a thermoelastic panel supported at the edges of the considered span. The problem of optimal suppression of vibrations is formulated when applying active transverse influences to the panel. To solve the optimization problem, modern methods developed in the theory of control of systems with distributed parameters described by partial differential equations are used.

  19. Optimization of controlled processes in combined-cycle plant (new developments and researches)

    NASA Astrophysics Data System (ADS)

    Tverskoy, Yu S.; Muravev, I. K.

    2017-11-01

    All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

  20. 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.

  1. Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

    NASA Technical Reports Server (NTRS)

    Zhao, Yiyuan; Chen, Robert T. N.

    1996-01-01

    This paper presents a summary of a series of recent analytical studies conducted to investigate One-Engine-Inoperative (OEI) optimal control strategies and the associated optimal trajectories for a twin engine helicopter in Category-A terminal-area operations. These studies also examine the associated heliport size requirements and the maximum gross weight capability of the helicopter. Using an eight states, two controls, augmented point-mass model representative of the study helicopter, Continued TakeOff (CTO), Rejected TakeOff (RTO), Balked Landing (BL), and Continued Landing (CL) are investigated for both Vertical-TakeOff-and-Landing (VTOL) and Short-TakeOff-and-Landing (STOL) terminal-area operations. The formulation of the nonlinear optimal control problems with considerations for realistic constraints, solution methods for the two-point boundary-value problem, a new real-time generation method for the optimal OEI trajectories, and the main results of this series of trajectory optimization studies are presented. In particular, a new balanced- weight concept for determining the takeoff decision point for VTOL Category-A operations is proposed, extending the balanced-field length concept used for STOL operations.

  2. Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories.

    PubMed

    Faruque, Imraan A; Muijres, Florian T; Macfarlane, Kenneth M; Kehlenbeck, Andrew; Humbert, J Sean

    2018-06-01

    This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

  3. Revenue Share between Layers and Investment Incentive for ISP in the Internet Market

    NASA Astrophysics Data System (ADS)

    Unno, Masaru; Xu, Hua

    In this paper, we consider a revenue-sharing and network investment problem between an Internet service provider (ISP) and a content provider (CP) by applying the dynamic agency theory. We formulate the problem as the principal-agent problem where the ISP is the principal and the CP is the agent. The principal-agent problem is transformed to a stochastic optimal control problem in which the objectives of ISP are to find an optimal revenue-sharing strategy and a network investment strategy, and to advise an incentive compatible effort level to the CP. The sufficient conditions for the existence of the optimal revenue-sharing strategy, the optimal investment strategy and the incentive compatible effort to the CP are obtained. A numerical example is solved to show the existence of such strategies. The practical implications of the results obtained in the paper will also be discussed.

  4. A Gradient-Based Multistart Algorithm for Multimodal Aerodynamic Shape Optimization Problems Based on Free-Form Deformation

    NASA Astrophysics Data System (ADS)

    Streuber, Gregg Mitchell

    Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.

  5. Optimal Low Energy Earth-Moon Transfers

    NASA Technical Reports Server (NTRS)

    Griesemer, Paul Ricord; Ocampo, Cesar; Cooley, D. S.

    2010-01-01

    The optimality of a low-energy Earth-Moon transfer is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the ballistic lunar capture trajectory is examined to determine whether one or more additional impulses may improve on the cost of the transfer.

  6. Model-Free Primitive-Based Iterative Learning Control Approach to Trajectory Tracking of MIMO Systems With Experimental Validation.

    PubMed

    Radac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M

    2015-11-01

    This paper proposes a novel model-free trajectory tracking of multiple-input multiple-output (MIMO) systems by the combination of iterative learning control (ILC) and primitives. The optimal trajectory tracking solution is obtained in terms of previously learned solutions to simple tasks called primitives. The library of primitives that are stored in memory consists of pairs of reference input/controlled output signals. The reference input primitives are optimized in a model-free ILC framework without using knowledge of the controlled process. The guaranteed convergence of the learning scheme is built upon a model-free virtual reference feedback tuning design of the feedback decoupling controller. Each new complex trajectory to be tracked is decomposed into the output primitives regarded as basis functions. The optimal reference input for the control system to track the desired trajectory is next recomposed from the reference input primitives. This is advantageous because the optimal reference input is computed straightforward without the need to learn from repeated executions of the tracking task. In addition, the optimization problem specific to trajectory tracking of square MIMO systems is decomposed in a set of optimization problems assigned to each separate single-input single-output control channel that ensures a convenient model-free decoupling. The new model-free primitive-based ILC approach is capable of planning, reasoning, and learning. A case study dealing with the model-free control tuning for a nonlinear aerodynamic system is included to validate the new approach. The experimental results are given.

  7. Optimal orbit transfer suitable for large flexible structures

    NASA Technical Reports Server (NTRS)

    Chatterjee, Alok K.

    1989-01-01

    The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.

  8. Symmetries in vakonomic dynamics: applications to optimal control

    NASA Astrophysics Data System (ADS)

    Martínez, Sonia; Cortés, Jorge; de León, Manuel

    2001-06-01

    Symmetries in vakonomic dynamics are discussed. Appropriate notions are introduced and their relationship with previous work on symmetries of singular Lagrangian systems is shown. Some Noether-type theorems are obtained. The results are applied to a class of general optimal control problems and to kinematic locomotion systems.

  9. Inventory Control System for a Healthcare Apparel Service Centre with Stockout Risk: A Case Analysis

    PubMed Central

    Hui, Chi-Leung

    2017-01-01

    Based on the real-world inventory control problem of a capacitated healthcare apparel service centre in Hong Kong which provides tailor-made apparel-making services for the elderly and disabled people, this paper studies a partial backordered continuous review inventory control problem in which the product demand follows a Poisson process with a constant lead time. The system is controlled by an (Q,r) inventory policy which incorporate the stockout risk, storage capacity, and partial backlog. The healthcare apparel service centre, under the capacity constraint, aims to minimize the inventory cost and achieving a low stockout risk. To address this challenge, an optimization problem is constructed. A real case-based data analysis is conducted, and the result shows that the expected total cost on an order cycle is reduced substantially at around 20% with our proposed optimal inventory control policy. An extensive sensitivity analysis is conducted to generate additional insights. PMID:29527283

  10. Coordinative Voltage Control Strategy with Multiple Resources for Distribution Systems of High PV Penetration: Preprint

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

    Zhu, Xiangqi; Zhang, Yingchen

    This paper presents an optimal voltage control methodology with coordination among different voltage-regulating resources, including controllable loads, distributed energy resources such as energy storage and photovoltaics (PV), and utility voltage-regulating devices such as voltage regulators and capacitors. The proposed methodology could effectively tackle the overvoltage and voltage regulation device distortion problems brought by high penetrations of PV to improve grid operation reliability. A voltage-load sensitivity matrix and voltage-regulator sensitivity matrix are used to deploy the resources along the feeder to achieve the control objectives. Mixed-integer nonlinear programming is used to solve the formulated optimization control problem. The methodology has beenmore » tested on the IEEE 123-feeder test system, and the results demonstrate that the proposed approach could actively tackle the voltage problem brought about by high penetrations of PV and improve the reliability of distribution system operation.« less

  11. Inventory Control System for a Healthcare Apparel Service Centre with Stockout Risk: A Case Analysis.

    PubMed

    Pan, An; Hui, Chi-Leung

    2017-01-01

    Based on the real-world inventory control problem of a capacitated healthcare apparel service centre in Hong Kong which provides tailor-made apparel-making services for the elderly and disabled people, this paper studies a partial backordered continuous review inventory control problem in which the product demand follows a Poisson process with a constant lead time. The system is controlled by an ( Q , r ) inventory policy which incorporate the stockout risk, storage capacity, and partial backlog. The healthcare apparel service centre, under the capacity constraint, aims to minimize the inventory cost and achieving a low stockout risk. To address this challenge, an optimization problem is constructed. A real case-based data analysis is conducted, and the result shows that the expected total cost on an order cycle is reduced substantially at around 20% with our proposed optimal inventory control policy. An extensive sensitivity analysis is conducted to generate additional insights.

  12. Control of functional differential equations to target sets in function space

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kent, G. A.

    1971-01-01

    Optimal control of systems governed by functional differential equations of retarded and neutral type is considered. Problems with function space initial and terminal manifolds are investigated. Existence of optimal controls, regularity, and bang-bang properties are discussed. Necessary and sufficient conditions are derived, and several solved examples which illustrate the theory are presented.

  13. Optimal clustering of MGs based on droop controller for improving reliability using a hybrid of harmony search and genetic algorithms.

    PubMed

    Abedini, Mohammad; Moradi, Mohammad H; Hosseinian, S M

    2016-03-01

    This paper proposes a novel method to address reliability and technical problems of microgrids (MGs) based on designing a number of self-adequate autonomous sub-MGs via adopting MGs clustering thinking. In doing so, a multi-objective optimization problem is developed where power losses reduction, voltage profile improvement and reliability enhancement are considered as the objective functions. To solve the optimization problem a hybrid algorithm, named HS-GA, is provided, based on genetic and harmony search algorithms, and a load flow method is given to model different types of DGs as droop controller. The performance of the proposed method is evaluated in two case studies. The results provide support for the performance of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Optimization of block-floating-point realizations for digital controllers with finite-word-length considerations.

    PubMed

    Wu, Jun; Hu, Xie-he; Chen, Sheng; Chu, Jian

    2003-01-01

    The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

  15. Stochastic Optimization For Water Resources Allocation

    NASA Astrophysics Data System (ADS)

    Yamout, G.; Hatfield, K.

    2003-12-01

    For more than 40 years, water resources allocation problems have been addressed using deterministic mathematical optimization. When data uncertainties exist, these methods could lead to solutions that are sub-optimal or even infeasible. While optimization models have been proposed for water resources decision-making under uncertainty, no attempts have been made to address the uncertainties in water allocation problems in an integrated approach. This paper presents an Integrated Dynamic, Multi-stage, Feedback-controlled, Linear, Stochastic, and Distributed parameter optimization approach to solve a problem of water resources allocation. It attempts to capture (1) the conflict caused by competing objectives, (2) environmental degradation produced by resource consumption, and finally (3) the uncertainty and risk generated by the inherently random nature of state and decision parameters involved in such a problem. A theoretical system is defined throughout its different elements. These elements consisting mainly of water resource components and end-users are described in terms of quantity, quality, and present and future associated risks and uncertainties. Models are identified, modified, and interfaced together to constitute an integrated water allocation optimization framework. This effort is a novel approach to confront the water allocation optimization problem while accounting for uncertainties associated with all its elements; thus resulting in a solution that correctly reflects the physical problem in hand.

  16. Continuous performance measurement in flight systems. [sequential control model

    NASA Technical Reports Server (NTRS)

    Connelly, E. M.; Sloan, N. A.; Zeskind, R. M.

    1975-01-01

    The desired response of many man machine control systems can be formulated as a solution to an optimal control synthesis problem where the cost index is given and the resulting optimal trajectories correspond to the desired trajectories of the man machine system. Optimal control synthesis provides the reference criteria and the significance of error information required for performance measurement. The synthesis procedure described provides a continuous performance measure (CPM) which is independent of the mechanism generating the control action. Therefore, the technique provides a meaningful method for online evaluation of man's control capability in terms of total man machine performance.

  17. Controllability of semi-infinite rod heating by a point source

    NASA Astrophysics Data System (ADS)

    Khurshudyan, A.

    2018-04-01

    The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

  18. Information distribution in distributed microprocessor based flight control systems

    NASA Technical Reports Server (NTRS)

    Montgomery, R. C.; Lee, P. S.

    1977-01-01

    This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

  19. 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

  20. Optimal control of 2-wheeled mobile robot at energy performance index

    NASA Astrophysics Data System (ADS)

    Kaliński, Krzysztof J.; Mazur, Michał

    2016-03-01

    The paper presents the application of the optimal control method at the energy performance index towards motion control of the 2-wheeled mobile robot. With the use of the proposed method of control the 2-wheeled mobile robot can realise effectively the desired trajectory. The problem of motion control of mobile robots is usually neglected and thus performance of the realisation of the high level control tasks is limited.

  1. 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.

  2. 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.

  3. Singular Optimal Controls of Rocket Motion (Survey)

    NASA Astrophysics Data System (ADS)

    Kiforenko, B. N.

    2017-05-01

    Survey of modern state and discussion of problems of the perfection of methods of investigation of variational problems with a focus on mechanics of space flight are presented. The main attention is paid to the enhancement of the methods of solving of variational problems of rocket motion in the gravitational fields, including rocket motion in the atmosphere. These problems are directly connected with the permanently actual problem of the practical astronautics to increase the payload that is orbited by the carrier rockets in the circumplanetary orbits. An analysis of modern approaches to solving the problems of control of rockets and spacecraft motion on the trajectories with singular arcs that are optimal for the motion of the variable mass body in the medium with resistance is given. The presented results for some maneuvers can serve as an information source for decision making on designing promising rocket and space technology

  4. ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1994-01-01

    This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1989. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

  5. ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

    NASA Technical Reports Server (NTRS)

    Frisch, H.

    1994-01-01

    This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1986. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

  6. Structures vibration control via Tuned Mass Dampers using a co-evolution Coral Reefs Optimization algorithm

    NASA Astrophysics Data System (ADS)

    Salcedo-Sanz, S.; Camacho-Gómez, C.; Magdaleno, A.; Pereira, E.; Lorenzana, A.

    2017-04-01

    In this paper we tackle a problem of optimal design and location of Tuned Mass Dampers (TMDs) for structures subjected to earthquake ground motions, using a novel meta-heuristic algorithm. Specifically, the Coral Reefs Optimization (CRO) with Substrate Layer (CRO-SL) is proposed as a competitive co-evolution algorithm with different exploration procedures within a single population of solutions. The proposed approach is able to solve the TMD design and location problem, by exploiting the combination of different types of searching mechanisms. This promotes a powerful evolutionary-like algorithm for optimization problems, which is shown to be very effective in this particular problem of TMDs tuning. The proposed algorithm's performance has been evaluated and compared with several reference algorithms in two building models with two and four floors, respectively.

  7. 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.

  8. Control theory based airfoil design using the Euler equations

    NASA Technical Reports Server (NTRS)

    Jameson, Antony; Reuther, James

    1994-01-01

    This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

  9. Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

    PubMed

    Sun, Kangkang; Sui, Shuai; Tong, Shaocheng

    2018-04-01

    This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

  10. Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes

    PubMed Central

    Dobos, László; Király, András; Abonyi, János

    2012-01-01

    Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. PMID:23213298

  11. OTIS 3.2 Software Released

    NASA Technical Reports Server (NTRS)

    Riehl, John P.; Sjauw, Waldy K.

    2004-01-01

    Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

  12. Models of resource allocation optimization when solving the control problems in organizational systems

    NASA Astrophysics Data System (ADS)

    Menshikh, V.; Samorokovskiy, A.; Avsentev, O.

    2018-03-01

    The mathematical model of optimizing the allocation of resources to reduce the time for management decisions and algorithms to solve the general problem of resource allocation. The optimization problem of choice of resources in organizational systems in order to reduce the total execution time of a job is solved. This problem is a complex three-level combinatorial problem, for the solving of which it is necessary to implement the solution to several specific problems: to estimate the duration of performing each action, depending on the number of performers within the group that performs this action; to estimate the total execution time of all actions depending on the quantitative composition of groups of performers; to find such a distribution of the existing resource of performers in groups to minimize the total execution time of all actions. In addition, algorithms to solve the general problem of resource allocation are proposed.

  13. Benchmarking optimization software with COPS.

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

    Dolan, E.D.; More, J.J.

    2001-01-08

    The COPS test set provides a modest selection of difficult nonlinearly constrained optimization problems from applications in optimal design, fluid dynamics, parameter estimation, and optimal control. In this report we describe version 2.0 of the COPS problems. The formulation and discretization of the original problems have been streamlined and improved. We have also added new problems. The presentation of COPS follows the original report, but the description of the problems has been streamlined. For each problem we discuss the formulation of the problem and the structural data in Table 0.1 on the formulation. The aim of presenting this data ismore » to provide an approximate idea of the size and sparsity of the problem. We also include the results of computational experiments with the LANCELOT, LOQO, MINOS, and SNOPT solvers. These computational experiments differ from the original results in that we have deleted problems that were considered to be too easy. Moreover, in the current version of the computational experiments, each problem is tested with four variations. An important difference between this report and the original report is that the tables that present the computational experiments are generated automatically from the testing script. This is explained in more detail in the report.« less

  14. Three-Axis Time-Optimal Attitude Maneuvers of a Rigid-Body

    NASA Astrophysics Data System (ADS)

    Wang, Xijing; Li, Jisheng

    With the development trends for modern satellites towards macro-scale and micro-scale, new demands are requested for its attitude adjustment. Precise pointing control and rapid maneuvering capabilities have long been part of many space missions. While the development of computer technology enables new optimal algorithms being used continuously, a powerful tool for solving problem is provided. Many papers about attitude adjustment have been published, the configurations of the spacecraft are considered rigid body with flexible parts or gyrostate-type systems. The object function always include minimum time or minimum fuel. During earlier satellite missions, the attitude acquisition was achieved by using the momentum ex change devices, performed by a sequential single-axis slewing strategy. Recently, the simultaneous three-axis minimum-time maneuver(reorientation) problems have been studied by many researchers. It is important to research the minimum-time maneuver of a rigid spacecraft within onboard power limits, because of potential space application such as surveying multiple targets in space and academic value. The minimum-time maneuver of a rigid spacecraft is a basic problem because the solutions for maneuvering flexible spacecraft are based on the solution to the rigid body slew problem. A new method for the open-loop solution for a rigid spacecraft maneuver is presented. Having neglected all perturbation torque, the necessary conditions of spacecraft from one state to another state can be determined. There is difference between single-axis with multi-axis. For single- axis analytical solution is possible and the switching line passing through the state-space origin belongs to parabolic. For multi-axis, it is impossible to get analytical solution due to the dynamic coupling between the axes and must be solved numerically. Proved by modern research, Euler axis rotations are quasi-time-optimal in general. On the basis of minimum value principles, a research for reorienting an inertial syrnmetric spacecraft with time cost function from an initial state of rest to a final state of rest is deduced. And the solution to it is stated below: Firstly, the essential condition for solving the problem is deduced with the minimum value principle. The necessary conditions for optimality yield a two point boundary-value problem (TPBVP), which, when solved, produces the control history that minimize time performance index. In the nonsingular control, the solution is the' bang-bang maneuver. The control profile is characterized by Saturated controls for the entire maneuver. The singular control maybe existed. It is only singular in mathematics. According to physical principle, the bigger the mode of the control torque is, the shorter the time is. So saturated controls are used in singular control. Secondly, the control parameters are always in maximum, so the key problem is to determine switch point thus original problem is changed to find the changing time. By the use of adjusting the switch on/off time, the genetic algorithm, which is a new robust method is optimized to determine the switch features without the gyroscopic coupling. There is improvement upon the traditional GA in this research. The homotopy method to find the nonlinear algebra is based on rigorous topology continuum theory. Based on the idea of the homotopy, the relaxation parameters are introduced, and the switch point is figured out with simulated annealing. Computer simulation results using a rigid body show that the new method is feasible and efficient. A practical method of computing approximate solutions to the time-optimal control- switch times for rigid body reorientation has been developed.

  15. Simulation and optimization of an experimental membrane wastewater treatment plant using computational intelligence methods.

    PubMed

    Ludwig, T; Kern, P; Bongards, M; Wolf, C

    2011-01-01

    The optimization of relaxation and filtration times of submerged microfiltration flat modules in membrane bioreactors used for municipal wastewater treatment is essential for efficient plant operation. However, the optimization and control of such plants and their filtration processes is a challenging problem due to the underlying highly nonlinear and complex processes. This paper presents the use of genetic algorithms for this optimization problem in conjunction with a fully calibrated simulation model, as computational intelligence methods are perfectly suited to the nonconvex multi-objective nature of the optimization problems posed by these complex systems. The simulation model is developed and calibrated using membrane modules from the wastewater simulation software GPS-X based on the Activated Sludge Model No.1 (ASM1). Simulation results have been validated at a technical reference plant. They clearly show that filtration process costs for cleaning and energy can be reduced significantly by intelligent process optimization.

  16. Time-optimal control of the spacecraft trajectories in the Earth-Moon system

    NASA Astrophysics Data System (ADS)

    Starinova, O. L.; Fain, M. K.; Materova, I. L.

    2017-01-01

    This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.

  17. Torque-based optimal acceleration control for electric vehicle

    NASA Astrophysics Data System (ADS)

    Lu, Dongbin; Ouyang, Minggao

    2014-03-01

    The existing research of the acceleration control mainly focuses on an optimization of the velocity trajectory with respect to a criterion formulation that weights acceleration time and fuel consumption. The minimum-fuel acceleration problem in conventional vehicle has been solved by Pontryagin's maximum principle and dynamic programming algorithm, respectively. The acceleration control with minimum energy consumption for battery electric vehicle(EV) has not been reported. In this paper, the permanent magnet synchronous motor(PMSM) is controlled by the field oriented control(FOC) method and the electric drive system for the EV(including the PMSM, the inverter and the battery) is modeled to favor over a detailed consumption map. The analytical algorithm is proposed to analyze the optimal acceleration control and the optimal torque versus speed curve in the acceleration process is obtained. Considering the acceleration time, a penalty function is introduced to realize a fast vehicle speed tracking. The optimal acceleration control is also addressed with dynamic programming(DP). This method can solve the optimal acceleration problem with precise time constraint, but it consumes a large amount of computation time. The EV used in simulation and experiment is a four-wheel hub motor drive electric vehicle. The simulation and experimental results show that the required battery energy has little difference between the acceleration control solved by analytical algorithm and that solved by DP, and is greatly reduced comparing with the constant pedal opening acceleration. The proposed analytical and DP algorithms can minimize the energy consumption in EV's acceleration process and the analytical algorithm is easy to be implemented in real-time control.

  18. Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan

    2006-01-01

    This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

  19. Control of functional differential equations with function space boundary conditions.

    NASA Technical Reports Server (NTRS)

    Banks, H. T.

    1972-01-01

    The results of various authors dealing with problems involving functional differential equations with terminal conditions in function space are reviewed. The review includes not only very recent results, but also some little known results of Soviet mathematicians prior to 1970. Particular attention is given to results concerning controllability, existence of optimal controls, and necessary and sufficient conditions for optimality.

  20. An inverse dynamics approach to trajectory optimization for an aerospace plane

    NASA Technical Reports Server (NTRS)

    Lu, Ping

    1992-01-01

    An inverse dynamics approach for trajectory optimization is proposed. This technique can be useful in many difficult trajectory optimization and control problems. The application of the approach is exemplified by ascent trajectory optimization for an aerospace plane. Both minimum-fuel and minimax types of performance indices are considered. When rocket augmentation is available for ascent, it is shown that accurate orbital insertion can be achieved through the inverse control of the rocket in the presence of disturbances.

  1. 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.

  2. The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model

    NASA Astrophysics Data System (ADS)

    Yang, Lu-Xing; Draief, Moez; Yang, Xiaofan

    2016-05-01

    Dynamic immunizations, under which the state of the propagation network of electronic viruses can be changed by adjusting the control measures, are regarded as an alternative to static immunizations. This paper addresses the optimal dynamical immunization under the widely accepted SIRS assumption. First, based on a controlled heterogeneous node-based SIRS model, an optimal control problem capturing the optimal dynamical immunization is formulated. Second, the existence of an optimal dynamical immunization scheme is shown, and the corresponding optimality system is derived. Next, some numerical examples are given to show that an optimal immunization strategy can be worked out by numerically solving the optimality system, from which it is found that the network topology has a complex impact on the optimal immunization strategy. Finally, the difference between a payoff and the minimum payoff is estimated in terms of the deviation of the corresponding immunization strategy from the optimal immunization strategy. The proposed optimal immunization scheme is justified, because it can achieve a low level of infections at a low cost.

  3. Optimal control of first order distributed systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Johnson, T. L.

    1972-01-01

    The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

  4. An approach to design controllers for MIMO fractional-order plants based on parameter optimization algorithm.

    PubMed

    Xue, Dingyü; Li, Tingxue

    2017-04-27

    The parameter optimization method for multivariable systems is extended to the controller design problems for multiple input multiple output (MIMO) square fractional-order plants. The algorithm can be applied to search for the optimal parameters of integer-order controllers for fractional-order plants with or without time delays. Two examples are given to present the controller design procedures for MIMO fractional-order systems. Simulation studies show that the integer-order controllers designed are robust to plant gain variations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  5. Optimal Damping of Perturbations of Moving Thermoelastic Panel

    NASA Astrophysics Data System (ADS)

    Banichuk, N. V.; Ivanova, S. Yu.

    2018-01-01

    The translational motion of a thermoelastic web subject to transverse vibrations caused by initial perturbations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic panel simply supported at its ends. The problem of optimal damping of vibrations when applying active transverse actions is formulated. For solving the optimization problem, modern methods developed in control theory for systems with distributed parameters described by partial differential equations are used.

  6. Optimization Strategies for Sensor and Actuator Placement

    NASA Technical Reports Server (NTRS)

    Padula, Sharon L.; Kincaid, Rex K.

    1999-01-01

    This paper provides a survey of actuator and sensor placement problems from a wide range of engineering disciplines and a variety of applications. Combinatorial optimization methods are recommended as a means for identifying sets of actuators and sensors that maximize performance. Several sample applications from NASA Langley Research Center, such as active structural acoustic control, are covered in detail. Laboratory and flight tests of these applications indicate that actuator and sensor placement methods are effective and important. Lessons learned in solving these optimization problems can guide future research.

  7. Global dynamic optimization approach to predict activation in metabolic pathways.

    PubMed

    de Hijas-Liste, Gundián M; Klipp, Edda; Balsa-Canto, Eva; Banga, Julio R

    2014-01-06

    During the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been successfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework. In this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results. The proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.

  8. Optimal Dynamic Advertising Strategy Under Age-Specific Market Segmentation

    NASA Astrophysics Data System (ADS)

    Krastev, Vladimir

    2011-12-01

    We consider the model proposed by Faggian and Grosset for determining the advertising efforts and goodwill in the long run of a company under age segmentation of consumers. Reducing this model to optimal control sub problems we find the optimal advertising strategy and goodwill.

  9. Optimal placement of FACTS devices using optimization techniques: A review

    NASA Astrophysics Data System (ADS)

    Gaur, Dipesh; Mathew, Lini

    2018-03-01

    Modern power system is dealt with overloading problem especially transmission network which works on their maximum limit. Today’s power system network tends to become unstable and prone to collapse due to disturbances. Flexible AC Transmission system (FACTS) provides solution to problems like line overloading, voltage stability, losses, power flow etc. FACTS can play important role in improving static and dynamic performance of power system. FACTS devices need high initial investment. Therefore, FACTS location, type and their rating are vital and should be optimized to place in the network for maximum benefit. In this paper, different optimization methods like Particle Swarm Optimization (PSO), Genetic Algorithm (GA) etc. are discussed and compared for optimal location, type and rating of devices. FACTS devices such as Thyristor Controlled Series Compensator (TCSC), Static Var Compensator (SVC) and Static Synchronous Compensator (STATCOM) are considered here. Mentioned FACTS controllers effects on different IEEE bus network parameters like generation cost, active power loss, voltage stability etc. have been analyzed and compared among the devices.

  10. Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

    NASA Technical Reports Server (NTRS)

    Hyland, D. C.; Bernstein, D. S.

    1987-01-01

    The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.

  11. 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.

  12. Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.

    PubMed

    Chang, Joshua; Paydarfar, David

    2014-12-01

    Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

  13. Guidance and control strategies for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Naidu, Desineni S.; Hibey, Joseph L.

    1988-01-01

    The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit. A performance index is chosen the minimize the fuel consumpltion for the transfer. Simulations are carried out for establishing a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the paper is the application of an efficient multiple shooting method for taming the notorious nonlinear, two-point, boundary value problem resulting from optimization procedure.

  14. Practical optimal flight control system design for helicopter aircraft. Volume 2: Software user's guide

    NASA Technical Reports Server (NTRS)

    Riedel, S. A.

    1979-01-01

    A method by which modern and classical control theory techniques may be integrated in a synergistic fashion and used in the design of practical flight control systems is presented. A general procedure is developed, and several illustrative examples are included. Emphasis is placed not only on the synthesis of the design, but on the assessment of the results as well. The first step is to establish the differences, distinguishing characteristics and connections between the modern and classical control theory approaches. Ultimately, this uncovers a relationship between bandwidth goals familiar in classical control and cost function weights in the equivalent optimal system. In order to obtain a practical optimal solution, it is also necessary to formulate the problem very carefully, and each choice of state, measurement and output variable must be judiciously considered. Once design goals are established and problem formulation completed, the control system is synthesized in a straightforward manner. Three steps are involved: filter-observer solution, regulator solution, and the combination of those two into the controller. Assessment of the controller permits and examination and expansion of the synthesis results.

  15. Analysis of explicit model predictive control for path-following control

    PubMed Central

    2018-01-01

    In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

  16. Analysis of explicit model predictive control for path-following control.

    PubMed

    Lee, Junho; Chang, Hyuk-Jun

    2018-01-01

    In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

  17. A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

    DOE PAGES

    D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; ...

    2015-12-21

    We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result,more » the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.« less

  18. Derived heuristics-based consistent optimization of material flow in a gold processing plant

    NASA Astrophysics Data System (ADS)

    Myburgh, Christie; Deb, Kalyanmoy

    2018-01-01

    Material flow in a chemical processing plant often follows complicated control laws and involves plant capacity constraints. Importantly, the process involves discrete scenarios which when modelled in a programming format involves if-then-else statements. Therefore, a formulation of an optimization problem of such processes becomes complicated with nonlinear and non-differentiable objective and constraint functions. In handling such problems using classical point-based approaches, users often have to resort to modifications and indirect ways of representing the problem to suit the restrictions associated with classical methods. In a particular gold processing plant optimization problem, these facts are demonstrated by showing results from MATLAB®'s well-known fmincon routine. Thereafter, a customized evolutionary optimization procedure which is capable of handling all complexities offered by the problem is developed. Although the evolutionary approach produced results with comparatively less variance over multiple runs, the performance has been enhanced by introducing derived heuristics associated with the problem. In this article, the development and usage of derived heuristics in a practical problem are presented and their importance in a quick convergence of the overall algorithm is demonstrated.

  19. An Optimization-based Atomistic-to-Continuum Coupling Method

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

    Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell

    2014-08-21

    In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally,more » we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.« less

  20. Adaptive Optimal Control Using Frequency Selective Information of the System Uncertainty With Application to Unmanned Aircraft.

    PubMed

    Maity, Arnab; Hocht, Leonhard; Heise, Christian; Holzapfel, Florian

    2018-01-01

    A new efficient adaptive optimal control approach is presented in this paper based on the indirect model reference adaptive control (MRAC) architecture for improvement of adaptation and tracking performance of the uncertain system. The system accounts here for both matched and unmatched unknown uncertainties that can act as plant as well as input effectiveness failures or damages. For adaptation of the unknown parameters of these uncertainties, the frequency selective learning approach is used. Its idea is to compute a filtered expression of the system uncertainty using multiple filters based on online instantaneous information, which is used for augmentation of the update law. It is capable of adjusting a sudden change in system dynamics without depending on high adaptation gains and can satisfy exponential parameter error convergence under certain conditions in the presence of structured matched and unmatched uncertainties as well. Additionally, the controller of the MRAC system is designed using a new optimal control method. This method is a new linear quadratic regulator-based optimal control formulation for both output regulation and command tracking problems. It provides a closed-form control solution. The proposed overall approach is applied in a control of lateral dynamics of an unmanned aircraft problem to show its effectiveness.

  1. A Sarsa(λ)-based control model for real-time traffic light coordination.

    PubMed

    Zhou, Xiaoke; Zhu, Fei; Liu, Quan; Fu, Yuchen; Huang, Wei

    2014-01-01

    Traffic problems often occur due to the traffic demands by the outnumbered vehicles on road. Maximizing traffic flow and minimizing the average waiting time are the goals of intelligent traffic control. Each junction wants to get larger traffic flow. During the course, junctions form a policy of coordination as well as constraints for adjacent junctions to maximize their own interests. A good traffic signal timing policy is helpful to solve the problem. However, as there are so many factors that can affect the traffic control model, it is difficult to find the optimal solution. The disability of traffic light controllers to learn from past experiences caused them to be unable to adaptively fit dynamic changes of traffic flow. Considering dynamic characteristics of the actual traffic environment, reinforcement learning algorithm based traffic control approach can be applied to get optimal scheduling policy. The proposed Sarsa(λ)-based real-time traffic control optimization model can maintain the traffic signal timing policy more effectively. The Sarsa(λ)-based model gains traffic cost of the vehicle, which considers delay time, the number of waiting vehicles, and the integrated saturation from its experiences to learn and determine the optimal actions. The experiment results show an inspiring improvement in traffic control, indicating the proposed model is capable of facilitating real-time dynamic traffic control.

  2. Multimodal optimization by using hybrid of artificial bee colony algorithm and BFGS algorithm

    NASA Astrophysics Data System (ADS)

    Anam, S.

    2017-10-01

    Optimization has become one of the important fields in Mathematics. Many problems in engineering and science can be formulated into optimization problems. They maybe have many local optima. The optimization problem with many local optima, known as multimodal optimization problem, is how to find the global solution. Several metaheuristic methods have been proposed to solve multimodal optimization problems such as Particle Swarm Optimization (PSO), Genetics Algorithm (GA), Artificial Bee Colony (ABC) algorithm, etc. The performance of the ABC algorithm is better than or similar to those of other population-based algorithms with the advantage of employing a fewer control parameters. The ABC algorithm also has the advantages of strong robustness, fast convergence and high flexibility. However, it has the disadvantages premature convergence in the later search period. The accuracy of the optimal value cannot meet the requirements sometimes. Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a good iterative method for finding a local optimum. Compared with other local optimization methods, the BFGS algorithm is better. Based on the advantages of the ABC algorithm and the BFGS algorithm, this paper proposes a hybrid of the artificial bee colony algorithm and the BFGS algorithm to solve the multimodal optimization problem. The first step is that the ABC algorithm is run to find a point. In the second step is that the point obtained by the first step is used as an initial point of BFGS algorithm. The results show that the hybrid method can overcome from the basic ABC algorithm problems for almost all test function. However, if the shape of function is flat, the proposed method cannot work well.

  3. 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.

  4. A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour

    NASA Technical Reports Server (NTRS)

    Leyland, Jane Anne

    1996-01-01

    Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.

  5. Finite element solution of optimal control problems with inequality constraints

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.

    1990-01-01

    A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

  6. Noniterative computation of infimum in H(infinity) optimisation for plants with invariant zeros on the j(omega)-axis

    NASA Technical Reports Server (NTRS)

    Chen, B. M.; Saber, A.

    1993-01-01

    A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem is presented, as a continuation of our earlier work. Our problem formulation is general and we do not place any restrictions in the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j(omega) axis.

  7. Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Salas, Manuel D.

    1997-01-01

    We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

  8. Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

    NASA Astrophysics Data System (ADS)

    Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

    2017-04-01

    Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

  9. Opitmal Platform Strategies in the Smartphone Market

    NASA Astrophysics Data System (ADS)

    Unno, Masaru; Xu, Hua

    In a smartphone market, smartphone makers encourage smartphone application providers (AP) to create more popular smartphone applications through making a revenue-sharing contract with AP and providing application-purchasing support to end users. In this paper, we study revenue-sharing and application-purchasing support problem between a risk-averse smartphone maker and a smartphone application provider. The problem is formulated as the smartphone makers's risk-sensitive stochastic control problem. The sufficient conditions for the existence of the optimal revenue-sharing strategy, the optimal application-purchasing support strategy and the incentive compatible effort recommended to AP are obtained. The effects of the smartphone makers's risk-sensitivity on the optimal strategies are also discussed. A numerical example is solved to show the computation aspects of the problem.

  10. Deadlock-free genetic scheduling algorithm for automated manufacturing systems based on deadlock control policy.

    PubMed

    Xing, KeYi; Han, LiBin; Zhou, MengChu; Wang, Feng

    2012-06-01

    Deadlock-free control and scheduling are vital for optimizing the performance of automated manufacturing systems (AMSs) with shared resources and route flexibility. Based on the Petri net models of AMSs, this paper embeds the optimal deadlock avoidance policy into the genetic algorithm and develops a novel deadlock-free genetic scheduling algorithm for AMSs. A possible solution of the scheduling problem is coded as a chromosome representation that is a permutation with repetition of parts. By using the one-step look-ahead method in the optimal deadlock control policy, the feasibility of a chromosome is checked, and infeasible chromosomes are amended into feasible ones, which can be easily decoded into a feasible deadlock-free schedule. The chromosome representation and polynomial complexity of checking and amending procedures together support the cooperative aspect of genetic search for scheduling problems strongly.

  11. Distributed Constrained Optimization with Semicoordinate Transformations

    NASA Technical Reports Server (NTRS)

    Macready, William; Wolpert, David

    2006-01-01

    Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

  12. 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.

  13. Automated trajectory planning for multiple-flyby interplanetary missions

    NASA Astrophysics Data System (ADS)

    Englander, Jacob

    Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both real-valued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the real-valued variables will represent the launch date, ight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. The contribution of this work is a framework for the autonomous optimization of multiple-flyby interplanetary trajectories. The trajectory design problem is converted into a HOCP with two nested loops: an "outer-loop" that finds the sequence of flybys and an "inner-loop" that optimizes the trajectory for each candidate yby sequence. The problem of choosing a sequence of flybys is posed as an integer programming problem and solved using a genetic algorithm (GA). This is an especially difficult problem to solve because GAs normally operate on a fixed-length set of decision variables. Since in interplanetary trajectory design the number of flyby maneuvers is not known a priori, it was necessary to devise a method of parameterizing the problem such that the GA can evolve a variable-length sequence of flybys. A novel "null gene" transcription was developed to meet this need. Then, for each candidate sequence of flybys, a trajectory must be found that visits each of the flyby targets and arrives at the final destination while optimizing some cost metric, such as minimizing ▵v or maximizing the final mass of the spacecraft. Three different classes of trajectory are described in this work, each of which requireda different physical model and optimization method. The choice of a trajectory model and optimization method is especially challenging because of the nature of the hybrid optimal control problem. Because the trajectory optimization problem is generated in real time by the outer-loop, the inner-loop optimization algorithm cannot require any a priori information and must always return a solution. In addition, the upper and lower bounds on each decision variable cannot be chosen a priori by the user because the user has no way to know what problem will be solved. Instead a method of choosing upper and lower bounds via a set of simple rules was developed and used for all three types of trajectory optimization problem. Many optimization algorithms were tested and discarded until suitable algorithms were found for each type of trajectory. The first class of trajectories use chemical propulsion and may only apply a ▵v at the periapse of each flyby. These Multiple Gravity Assist (MGA) trajectories are optimized using a cooperative algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The second class of trajectories, known as Multiple Gravity Assist with one Deep Space Maneuver (MGA-DSM), also use chemical propulsion but instead of maneuvering at the periapse of each flyby as in the MGA case a maneuver is applied at a free point along each planet-to-planet arc, i.e. there is one maneuver for each pair of flybys. MGA-DSM trajectories are parameterized by more variables than MGA trajectories, and so the cooperative algorithm of DE and PSO that was used to optimize MGA trajectories was found to be less effective when applied to MGA-DSM. Instead, either PSO or DE alone were found to be more effective. The third class of trajectories addressed in this work are those using continuousthrust propulsion. Continuous-thrust trajectory optimization problems are more challenging than impulsive-thrust problems because the control variables are a continuous time series rather than a small set of parameters and because the spacecraft does not follow a conic section trajectory, leading to a large number of nonlinear constraints that must be satisfied to ensure that the spacecraft obeys the equations of motion. Many models and optimization algorithms were applied including direct transcription with nonlinear programming (DTNLP), the inverse-polynomial shapebased method, and feasible region analysis. However the only physical model and optimization method that proved reliable enough were the Sims-Flanagan transcription coupled with a nonlinear programming solver and the monotonic basin hopping (MBH) global search heuristic. The methods developed here are demonstrated to optimize a set of example trajectories, including a recreation of the Cassini mission, a Galileo-like mission, and conceptual continuous-thrust missions to Jupiter, Mercury, and Uranus.

  14. Multi-objective design optimization and control of magnetorheological fluid brakes for automotive applications

    NASA Astrophysics Data System (ADS)

    Shamieh, Hadi; Sedaghati, Ramin

    2017-12-01

    The magnetorheological brake (MRB) is an electromechanical device that generates a retarding torque through employing magnetorheological (MR) fluids. The objective of this paper is to design, optimize and control an MRB for automotive applications considering. The dynamic range of a disk-type MRB expressing the ratio of generated toque at on and off states has been formulated as a function of the rotational speed, geometrical and material properties, and applied electrical current. Analytical magnetic circuit analysis has been conducted to derive the relation between magnetic field intensity and the applied electrical current as a function of the MRB geometrical and material properties. A multidisciplinary design optimization problem has then been formulated to identify the optimal brake geometrical parameters to maximize the dynamic range and minimize the response time and weight of the MRB under weight, size and magnetic flux density constraints. The optimization problem has been solved using combined genetic and sequential quadratic programming algorithms. Finally, the performance of the optimally designed MRB has been investigated in a quarter vehicle model. A PID controller has been designed to regulate the applied current required by the MRB in order to improve vehicle’s slipping on different road conditions.

  15. An optimizing start-up strategy for a bio-methanator.

    PubMed

    Sbarciog, Mihaela; Loccufier, Mia; Vande Wouwer, Alain

    2012-05-01

    This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang-bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.

  16. Quasivelocities and Optimal Control for underactuated Mechanical Systems

    NASA Astrophysics Data System (ADS)

    Colombo, L.; de Diego, D. Martín

    2010-07-01

    This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system subjected to constraints. The equations of motion are geometrically derived using an adaptation of the classical Skinner and Rusk formalism.

  17. Quasivelocities and Optimal Control for underactuated Mechanical Systems

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

    Colombo, L.; Martin de Diego, D.

    2010-07-28

    This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system subjected to constraints. The equations of motion are geometrically derived using an adaptation of the classical Skinner and Rusk formalism.

  18. Optimization of Airport Surface Traffic: A Case-Study of Incheon International Airport

    NASA Technical Reports Server (NTRS)

    Eun, Yeonju; Jeon, Daekeun; Lee, Hanbong; Jung, Yoon C.; Zhu, Zhifan; Jeong, Myeongsook; Kim, Hyounkong; Oh, Eunmi; Hong, Sungkwon

    2017-01-01

    This study aims to develop a controllers decision support tool for departure and surface management of ICN. Airport surface traffic optimization for Incheon International Airport (ICN) in South Korea was studied based on the operational characteristics of ICN and airspace of Korea. For surface traffic optimization, a multiple runway scheduling problem and a taxi scheduling problem were formulated into two Mixed Integer Linear Programming (MILP) optimization models. The Miles-In-Trail (MIT) separation constraint at the departure fix shared by the departure flights from multiple runways and the runway crossing constraints due to the taxi route configuration specific to ICN were incorporated into the runway scheduling and taxiway scheduling problems, respectively. Since the MILP-based optimization model for the multiple runway scheduling problem may be computationally intensive, computation times and delay costs of different solving methods were compared for a practical implementation. This research was a collaboration between Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA).

  19. Optimization of Airport Surface Traffic: A Case-Study of Incheon International Airport

    NASA Technical Reports Server (NTRS)

    Eun, Yeonju; Jeon, Daekeun; Lee, Hanbong; Jung, Yoon Chul; Zhu, Zhifan; Jeong, Myeong-Sook; Kim, Hyoun Kyoung; Oh, Eunmi; Hong, Sungkwon

    2017-01-01

    This study aims to develop a controllers' decision support tool for departure and surface management of ICN. Airport surface traffic optimization for Incheon International Airport (ICN) in South Korea was studied based on the operational characteristics of ICN and airspace of Korea. For surface traffic optimization, a multiple runway scheduling problem and a taxi scheduling problem were formulated into two Mixed Integer Linear Programming (MILP) optimization models. The Miles-In-Trail (MIT) separation constraint at the departure fix shared by the departure flights from multiple runways and the runway crossing constraints due to the taxi route configuration specific to ICN were incorporated into the runway scheduling and taxiway scheduling problems, respectively. Since the MILP-based optimization model for the multiple runway scheduling problem may be computationally intensive, computation times and delay costs of different solving methods were compared for a practical implementation. This research was a collaboration between Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA).

  20. A direct method for synthesizing low-order optimal feedback control laws with application to flutter suppression

    NASA Technical Reports Server (NTRS)

    Mukhopadhyay, V.; Newsom, J. R.; Abel, I.

    1980-01-01

    A direct method of synthesizing a low-order optimal feedback control law for a high order system is presented. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean square steady state responses and control inputs. The controller is shown to be equivalent to a partial state estimator. The method is applied to the problem of active flutter suppression. Numerical results are presented for a 20th order system representing an aeroelastic wind-tunnel wing model. Low-order controllers (fourth and sixth order) are compared with a full order (20th order) optimal controller and found to provide near optimal performance with adequate stability margins.

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