Management of occupational exposure to engineered nanoparticles through a chance-constrained nonlinear programming approach.

PubMed

Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin

2013-03-26

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties.

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.

A hybrid nonlinear programming method for design optimization

NASA Technical Reports Server (NTRS)

Rajan, S. D.

1986-01-01

Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.

OPTIMIZATION OF COUNTERCURRENT STAGED PROCESSES.

DTIC Science & Technology

CHEMICAL ENGINEERING , OPTIMIZATION), (*DISTILLATION, OPTIMIZATION), INDUSTRIAL PRODUCTION, INDUSTRIAL EQUIPMENT, MATHEMATICAL MODELS, DIFFERENCE EQUATIONS, NONLINEAR PROGRAMMING, BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION

Nonlinear program based optimization of boost and buck-boost converter designs

NASA Astrophysics Data System (ADS)

Rahman, S.; Lee, F. C.

The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.

CSOLNP: Numerical Optimization Engine for Solving Non-linearly Constrained Problems.

PubMed

Zahery, Mahsa; Maes, Hermine H; Neale, Michael C

2017-08-01

We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package version, 1) alongside some improvements. CSOLNP solves non-linearly constrained optimization problems using a Sequential Quadratic Programming (SQP) algorithm. CSOLNP, NPSOL (a very popular implementation of SQP method in FORTRAN (Gill et al., 1986, User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming (No. SOL-86-2). Stanford, CA: Stanford University Systems Optimization Laboratory), and SLSQP (another SQP implementation available as part of the NLOPT collection (Johnson, 2014, The NLopt nonlinear-optimization package. Retrieved from http://ab-initio.mit.edu/nlopt)) are three optimizers available in OpenMx package. These optimizers are compared in terms of runtimes, final objective values, and memory consumption. A Monte Carlo analysis of the performance of the optimizers was performed on ordinal and continuous models with five variables and one or two factors. While the relative difference between the objective values is less than 0.5%, CSOLNP is in general faster than NPSOL and SLSQP for ordinal analysis. As for continuous data, none of the optimizers performs consistently faster than the others. In terms of memory usage, we used Valgrind's heap profiler tool, called Massif, on one-factor threshold models. CSOLNP and NPSOL consume the same amount of memory, while SLSQP uses 71 MB more memory than the other two optimizers.

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.

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

PubMed

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

2011-01-01

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

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

NASA Astrophysics Data System (ADS)

Li, Shuang; Zhu, Yongsheng; Wang, Yukai

2014-02-01

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.

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.

Variable-Metric Algorithm For Constrained Optimization

NASA Technical Reports Server (NTRS)

Frick, James D.

1989-01-01

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

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.

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

PubMed

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

2011-12-01

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

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

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.

Multilevel algorithms for nonlinear optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Construction of pore network models for Berea and Fontainebleau sandstones using non-linear programing and optimization techniques

NASA Astrophysics Data System (ADS)

Sharqawy, Mostafa H.

2016-12-01

Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.

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.

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

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

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

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.

Structural Optimization for Reliability Using Nonlinear Goal Programming

NASA Technical Reports Server (NTRS)

El-Sayed, Mohamed E.

1999-01-01

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

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.

Nonlinear optimization with linear constraints using a projection method

NASA Technical Reports Server (NTRS)

Fox, T.

1982-01-01

Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

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

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

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

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.

2016-01-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C

2015-03-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

Optimal fabrication processes for unidirectional metal-matrix composites: A computational simulation

NASA Technical Reports Server (NTRS)

Saravanos, D. A.; Murthy, P. L. N.; Morel, M.

1990-01-01

A method is proposed for optimizing the fabrication process of unidirectional metal matrix composites. The temperature and pressure histories are optimized such that the residual microstresses of the composite at the end of the fabrication process are minimized and the material integrity throughout the process is ensured. The response of the composite during the fabrication is simulated based on a nonlinear micromechanics theory. The optimal fabrication problem is formulated and solved with non-linear programming. Application cases regarding the optimization of the fabrication cool-down phases of unidirectional ultra-high modulus graphite/copper and silicon carbide/titanium composites are presented.

Optimal fabrication processes for unidirectional metal-matrix composites - A computational simulation

NASA Technical Reports Server (NTRS)

Saravanos, D. A.; Murthy, P. L. N.; Morel, M.

1990-01-01

A method is proposed for optimizing the fabrication process of unidirectional metal matrix composites. The temperature and pressure histories are optimized such that the residual microstresses of the composite at the end of the fabrication process are minimized and the material integrity throughout the process is ensured. The response of the composite during the fabrication is simulated based on a nonlinear micromechanics theory. The optimal fabrication problem is formulated and solved with nonlinear programming. Application cases regarding the optimization of the fabrication cool-down phases of unidirectional ultra-high modulus graphite/copper and silicon carbide/titanium composites are presented.

Optimization of municipal pressure pumping station layout and sewage pipe network design

NASA Astrophysics Data System (ADS)

Tian, Jiandong; Cheng, Jilin; Gong, Yi

2018-03-01

Accelerated urbanization places extraordinary demands on sewer networks; thus optimization research to improve the design of these systems has practical significance. In this article, a subsystem nonlinear programming model is developed to optimize pumping station layout and sewage pipe network design. The subsystem model is expanded into a large-scale complex nonlinear programming system model to find the minimum total annual cost of the pumping station and network of all pipe segments. A comparative analysis is conducted using the sewage network in Taizhou City, China, as an example. The proposed method demonstrated that significant cost savings could have been realized if the studied system had been optimized using the techniques described in this article. Therefore, the method has practical value for optimizing urban sewage projects and provides a reference for theoretical research on optimization of urban drainage pumping station layouts.

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.

Operations research investigations of satellite power stations

NASA Technical Reports Server (NTRS)

Cole, J. W.; Ballard, J. L.

1976-01-01

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

A general-purpose optimization program for engineering design

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.; Sugimoto, H.

1986-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.

Large scale nonlinear programming for the optimization of spacecraft trajectories

NASA Astrophysics Data System (ADS)

Arrieta-Camacho, Juan Jose

Despite the availability of high fidelity mathematical models, the computation of accurate optimal spacecraft trajectories has never been an easy task. While simplified models of spacecraft motion can provide useful estimates on energy requirements, sizing, and cost; the actual launch window and maneuver scheduling must rely on more accurate representations. We propose an alternative for the computation of optimal transfers that uses an accurate representation of the spacecraft dynamics. Like other methodologies for trajectory optimization, this alternative is able to consider all major disturbances. In contrast, it can handle explicitly equality and inequality constraints throughout the trajectory; it requires neither the derivation of costate equations nor the identification of the constrained arcs. The alternative consist of two steps: (1) discretizing the dynamic model using high-order collocation at Radau points, which displays numerical advantages, and (2) solution to the resulting Nonlinear Programming (NLP) problem using an interior point method, which does not suffer from the performance bottleneck associated with identifying the active set, as required by sequential quadratic programming methods; in this way the methodology exploits the availability of sound numerical methods, and next generation NLP solvers. In practice the methodology is versatile; it can be applied to a variety of aerospace problems like homing, guidance, and aircraft collision avoidance; the methodology is particularly well suited for low-thrust spacecraft trajectory optimization. Examples are presented which consider the optimization of a low-thrust orbit transfer subject to the main disturbances due to Earth's gravity field together with Lunar and Solar attraction. Other example considers the optimization of a multiple asteroid rendezvous problem. In both cases, the ability of our proposed methodology to consider non-standard objective functions and constraints is illustrated. Future research directions are identified, involving the automatic scheduling and optimization of trajectory correction maneuvers. The sensitivity information provided by the methodology is expected to be invaluable in such research pursuit. The collocation scheme and nonlinear programming algorithm presented in this work, complement other existing methodologies by providing reliable and efficient numerical methods able to handle large scale, nonlinear dynamic models.

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.

Image reconstruction and scan configurations enabled by optimization-based algorithms in multispectral CT

NASA Astrophysics Data System (ADS)

Chen, Buxin; Zhang, Zheng; Sidky, Emil Y.; Xia, Dan; Pan, Xiaochuan

2017-11-01

Optimization-based algorithms for image reconstruction in multispectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In this work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for the standard scan configuration, the emphasis is on investigating the algorithm’s potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which has potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or x-ray illumination coverage in MCT.

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.

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Research on numerical method for multiple pollution source discharge and optimal reduction program

NASA Astrophysics Data System (ADS)

Li, Mingchang; Dai, Mingxin; Zhou, Bin; Zou, Bin

2018-03-01

In this paper, the optimal method for reduction program is proposed by the nonlinear optimal algorithms named that genetic algorithm. The four main rivers in Jiangsu province, China are selected for reducing the environmental pollution in nearshore district. Dissolved inorganic nitrogen (DIN) is studied as the only pollutant. The environmental status and standard in the nearshore district is used to reduce the discharge of multiple river pollutant. The research results of reduction program are the basis of marine environmental management.

Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints.

PubMed

Fan, Bo; Yang, Qinmin; Tang, Xiaoyu; Sun, Youxian

2018-06-01

In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.

Optimal stocking of species by diameter class for even-aged mid-to-late rotation Appalachian hardwoods

Treesearch

Joseph B. Roise; Joosang Chung; Chris B. LeDoux

1988-01-01

Nonlinear programming (NP) is applied to the problem of finding optimal thinning and harvest regimes simultaneously with species mix and diameter class distribution. Optimal results for given cases are reported. Results of the NP optimization are compared with prescriptions developed by Appalachian hardwood silviculturists.

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

Adaptive Critic Nonlinear Robust Control: A Survey.

PubMed

Wang, Ding; He, Haibo; Liu, Derong

2017-10-01

Adaptive dynamic programming (ADP) and reinforcement learning are quite relevant to each other when performing intelligent optimization. They are both regarded as promising methods involving important components of evaluation and improvement, at the background of information technology, such as artificial intelligence, big data, and deep learning. Although great progresses have been achieved and surveyed when addressing nonlinear optimal control problems, the research on robustness of ADP-based control strategies under uncertain environment has not been fully summarized. Hence, this survey reviews the recent main results of adaptive-critic-based robust control design of continuous-time nonlinear systems. The ADP-based nonlinear optimal regulation is reviewed, followed by robust stabilization of nonlinear systems with matched uncertainties, guaranteed cost control design of unmatched plants, and decentralized stabilization of interconnected systems. Additionally, further comprehensive discussions are presented, including event-based robust control design, improvement of the critic learning rule, nonlinear H ∞ control design, and several notes on future perspectives. By applying the ADP-based optimal and robust control methods to a practical power system and an overhead crane plant, two typical examples are provided to verify the effectiveness of theoretical results. Overall, this survey is beneficial to promote the development of adaptive critic control methods with robustness guarantee and the construction of higher level intelligent systems.

A Polyhedral Outer-approximation, Dynamic-discretization optimization solver, 1.x

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

Bent, Rusell; Nagarajan, Harsha; Sundar, Kaarthik

2017-09-25

In this software, we implement an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) to global optimality. The algorithm combines ideas that exploit the structure of convex relaxations to MINLPs and bound tightening procedures

A finite element code for electric motor design

NASA Technical Reports Server (NTRS)

Campbell, C. Warren

1994-01-01

FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.

Augmented Lagrange Programming Neural Network for Localization Using Time-Difference-of-Arrival Measurements.

PubMed

Han, Zifa; Leung, Chi Sing; So, Hing Cheung; Constantinides, Anthony George

2017-08-15

A commonly used measurement model for locating a mobile source is time-difference-of-arrival (TDOA). As each TDOA measurement defines a hyperbola, it is not straightforward to compute the mobile source position due to the nonlinear relationship in the measurements. This brief exploits the Lagrange programming neural network (LPNN), which provides a general framework to solve nonlinear constrained optimization problems, for the TDOA-based localization. The local stability of the proposed LPNN solution is also analyzed. Simulation results are included to evaluate the localization accuracy of the LPNN scheme by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

NASA Technical Reports Server (NTRS)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.; Kelly, Lon C.

2005-01-01

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Optimization by nonhierarchical asynchronous decomposition

NASA Technical Reports Server (NTRS)

Shankar, Jayashree; Ribbens, Calvin J.; Haftka, Raphael T.; Watson, Layne T.

1992-01-01

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness.

Optimization of a bundle divertor for FED

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

Hively, L.M.; Rothe, K.E.; Minkoff, M.

1982-01-01

Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

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

A multi-product green supply chain under government supervision with price and demand uncertainty

NASA Astrophysics Data System (ADS)

Hafezalkotob, Ashkan; Zamani, Soma

2018-05-01

In this paper, a bi-level game-theoretic model is proposed to investigate the effects of governmental financial intervention on green supply chain. This problem is formulated as a bi-level program for a green supply chain that produces various products with different environmental pollution levels. The problem is also regard uncertainties in market demand and sale price of raw materials and products. The model is further transformed into a single-level nonlinear programming problem by replacing the lower-level optimization problem with its Karush-Kuhn-Tucker optimality conditions. Genetic algorithm is applied as a solution methodology to solve nonlinear programming model. Finally, to investigate the validity of the proposed method, the computational results obtained through genetic algorithm are compared with global optimal solution attained by enumerative method. Analytical results indicate that the proposed GA offers better solutions in large size problems. Also, we conclude that financial intervention by government consists of green taxation and subsidization is an effective method to stabilize green supply chain members' performance.

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.

Manual of phosphoric acid fuel cell power plant optimization model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

NASA Astrophysics Data System (ADS)

Zhang, Huan; Dower, Peter M.

2012-09-01

Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

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.

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

An optimization model for the US Air-Traffic System

NASA Technical Reports Server (NTRS)

Mulvey, J. M.

1986-01-01

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

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.

Further developments in the controlled growth approach for optimal structural synthesis

NASA Technical Reports Server (NTRS)

Hajela, P.

1982-01-01

It is pointed out that the use of nonlinear programming methods in conjunction with finite element and other discrete analysis techniques have provided a powerful tool in the domain of optimal structural synthesis. The present investigation is concerned with new strategies which comprise an extension to the controlled growth method considered by Hajela and Sobieski-Sobieszczanski (1981). This method proposed an approach wherein the standard nonlinear programming (NLP) methodology of working with a very large number of design variables was replaced by a sequence of smaller optimization cycles, each involving a single 'dominant' variable. The current investigation outlines some new features. Attention is given to a modified cumulative constraint representation which is defined in both the feasible and infeasible domain of the design space. Other new features are related to the evaluation of the 'effectiveness measure' on which the choice of the dominant variable and the linking strategy is based.

Structural optimization of framed structures using generalized optimality criteria

NASA Technical Reports Server (NTRS)

Kolonay, R. M.; Venkayya, Vipperla B.; Tischler, V. A.; Canfield, R. A.

1989-01-01

The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

ADS: A FORTRAN program for automated design synthesis: Version 1.10

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.

1985-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired.

Optimization of Dynamic Aperture of PEP-X Baseline Design

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

Wang, Min-Huey; /SLAC; Cai, Yunhai

2010-08-23

SLAC is developing a long-range plan to transfer the evolving scientific programs at SSRL from the SPEAR3 light source to a much higher performing photon source. Storage ring design is one of the possibilities that would be housed in the 2.2-km PEP-II tunnel. The design goal of PEPX storage ring is to approach an optimal light source design with horizontal emittance less than 100 pm and vertical emittance of 8 pm to reach the diffraction limit of 1-{angstrom} x-ray. The low emittance design requires a lattice with strong focusing leading to high natural chromaticity and therefore to strong sextupoles. Themore » latter caused reduction of dynamic aperture. The dynamic aperture requirement for horizontal injection at injection point is about 10 mm. In order to achieve the desired dynamic aperture the transverse non-linearity of PEP-X is studied. The program LEGO is used to simulate the particle motion. The technique of frequency map is used to analyze the nonlinear behavior. The effect of the non-linearity is tried to minimize at the given constrains of limited space. The details and results of dynamic aperture optimization are discussed in this paper.« less

Structural, vibrational spectroscopic and nonlinear optical activity studies on 2-hydroxy- 3, 5-dinitropyridine: A DFT approach

NASA Astrophysics Data System (ADS)

Asath, R. Mohamed; Premkumar, S.; Jawahar, A.; Mathavan, T.; Dhas, M. Kumara; Benial, A. Milton Franklin

2015-06-01

The conformational analysis was carried out for 2-Hydroxy- 3, 5-dinitropyridine molecule using potential energy surface scan and the most stable optimized conformer was predicted. The vibrational frequencies and Mulliken atomic charge distribution were calculated for the optimized geometry of the molecule using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intramolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness values of the title molecule were carried out. The nonlinear optical activity of the molecule was studied by means of first order hyperpolarizability, which was computed as 7.64 times greater than urea. The natural bond orbital analysis was performed to confirm the nonlinear optical activity of the molecule.

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.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

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

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

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.

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.

Reentry trajectory optimization with waypoint and no-fly zone constraints using multiphase convex programming

NASA Astrophysics Data System (ADS)

Zhao, Dang-Jun; Song, Zheng-Yu

2017-08-01

This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

NASA Astrophysics Data System (ADS)

Wang, Liwei; Liu, Xinggao; Zhang, Zeyin

2017-02-01

An efficient primal-dual interior-point algorithm using a new non-monotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented.

Investigation on the use of optimization techniques for helicopter airframe vibrations design studies

NASA Technical Reports Server (NTRS)

Sreekanta Murthy, T.

1992-01-01

Results of the investigation of formal nonlinear programming-based numerical optimization techniques of helicopter airframe vibration reduction are summarized. The objective and constraint function and the sensitivity expressions used in the formulation of airframe vibration optimization problems are presented and discussed. Implementation of a new computational procedure based on MSC/NASTRAN and CONMIN in a computer program system called DYNOPT for optimizing airframes subject to strength, frequency, dynamic response, and dynamic stress constraints is described. An optimization methodology is proposed which is thought to provide a new way of applying formal optimization techniques during the various phases of the airframe design process. Numerical results obtained from the application of the DYNOPT optimization code to a helicopter airframe are discussed.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Generalized Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1983-04-11

existing ones. * -37- !I T-472 REFERENCES [1] Avriel, M., W. E. Diewert, S. Schaible and W. T. Ziemba (1981). Introduction to concave and generalized concave...functions. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba , eds.), Academic Press, New York, pp. 21-50. (21 Bank...Optimality conditions involving generalized convex mappings. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba

Robust optimization for nonlinear time-delay dynamical system of dha regulon with cost sensitivity constraint in batch culture

NASA Astrophysics Data System (ADS)

Yuan, Jinlong; Zhang, Xu; Liu, Chongyang; Chang, Liang; Xie, Jun; Feng, Enmin; Yin, Hongchao; Xiu, Zhilong

2016-09-01

Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear time-delay dynamical system of dha-regulonwith unknown time-delays in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumonia. Some important properties and strong positive invariance are discussed. Because of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, a quantitative biological robustness for the concentrations of intracellular substances is defined by penalizing a weighted sum of the expectation and variance of the relative deviation between system outputs before and after the time-delays are perturbed. Our goal is to determine optimal values of the time-delays. To this end, we formulate an optimization problem in which the time delays are decision variables and the cost function is to minimize the biological robustness. This optimization problem is subject to the time-delay system, parameter constraints, continuous state inequality constraints for ensuring that the concentrations of extracellular and intracellular substances lie within specified limits, a quality constraint to reflect operational requirements and a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved. It is approximated as a sequence of nonlinear programming sub-problems through the application of constraint transcription and local smoothing approximation techniques. Due to the highly complex nature of this optimization problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these nonlinear programming sub-problems based on the filled function method. Finally, it is observed that the obtained optimal estimates for the time-delays are highly satisfactory via numerical simulations.

Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1982-12-21

and W. T. ZIEMBA (1981). Intro- duction to concave and generalized concave functions. In Gener- alized Concavity in Optimization and Economics (S...Schaible and W. T. Ziemba , eds.), pp. 21-50. Academic Press, New York. BANK, B., J. GUDDAT, D. KLATTE, B. KUMMER, and K. TAMMER (1982). Non- Linear

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.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

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

PubMed

Wei, Qinglai; Liu, Derong; Lin, Hanquan

2016-03-01

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

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

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.

Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

NASA Astrophysics Data System (ADS)

Elliott, Louie C.

This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

Incorporation of Fixed Installation Costs into Optimization of Groundwater Remediation with a New Efficient Surrogate Nonlinear Mixed Integer Optimization Algorithm

NASA Astrophysics Data System (ADS)

Shoemaker, Christine; Wan, Ying

2016-04-01

Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).

Automatic design of synthetic gene circuits through mixed integer non-linear programming.

PubMed

Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias

2012-01-01

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Leake, R. J.; Sain, M. K.

1978-01-01

General goals of the research were classified into two categories. The first category involves the use of modern multivariable frequency domain methods for control of engine models in the neighborhood of a quiescent point. The second category involves the use of nonlinear modelling and optimization techniques for control of engine models over a more extensive part of the flight envelope. In the frequency domain category, works were published in the areas of low-interaction design, polynomial design, and multiple setpoint studies. A number of these ideas progressed to the point at which they are starting to attract practical interest. In the nonlinear category, advances were made both in engine modelling and in the details associated with software for determination of time optimal controls. Nonlinear models for a two spool turbofan engine were expanded and refined; and a promising new approach to automatic model generation was placed under study. A two time scale scheme was developed to do two-dimensional dynamic programming, and an outward spiral sweep technique has greatly speeded convergence times in time optimal calculations.

Indirect synthesis of multi-degree of freedom transient systems. [linear programming for a kinematically linear system

NASA Technical Reports Server (NTRS)

Pilkey, W. D.; Chen, Y. H.

1974-01-01

An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

Mixed integer nonlinear programming model of wireless pricing scheme with QoS attribute of bandwidth and end-to-end delay

NASA Astrophysics Data System (ADS)

Irmeilyana, Puspita, Fitri Maya; Indrawati

2016-02-01

The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

NASA Technical Reports Server (NTRS)

Kottapalli, Sesi; Leyland, Jane

2014-01-01

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

Comparison of penalty functions on a penalty approach to mixed-integer optimization

NASA Astrophysics Data System (ADS)

Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

2016-06-01

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

Ascent guidance algorithm using lidar wind measurements

NASA Technical Reports Server (NTRS)

Cramer, Evin J.; Bradt, Jerre E.; Hardtla, John W.

1990-01-01

The formulation of a general nonlinear programming guidance algorithm that incorporates wind measurements in the computation of ascent guidance steering commands is discussed. A nonlinear programming (NLP) algorithm that is designed to solve a very general problem has the potential to address the diversity demanded by future launch systems. Using B-splines for the command functional form allows the NLP algorithm to adjust the shape of the command profile to achieve optimal performance. The algorithm flexibility is demonstrated by simulation of ascent with dynamic loading constraints through a set of random wind profiles with and without wind sensing capability.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Topology optimization applied to the design of cooling channels for plastic injection

NASA Astrophysics Data System (ADS)

Muñoz, D. A.; Arango, J. P.; González, C.; Puerto, E.; Garzón, M.

2018-04-01

In this paper, topology optimization is applied to design cooling channels in a mold of structural steel. The problem was implemented in COMSOL multiphysics, where two physics were coupled, heat transfer and solid mechanics. The optimization objective is to maximize the conduction heat flux in the mold and minimize the deformations when the plastic is injected. In order to find an optimal geometry for this objective, a density-based method was implemented into the nonlinear program (NLP) for which feasible results were found.

Sizing of complex structure by the integration of several different optimal design algorithms

NASA Technical Reports Server (NTRS)

Sobieszczanski, J.

1974-01-01

Practical design of large-scale structures can be accomplished with the aid of the digital computer by bringing together in one computer program algorithms of nonlinear mathematical programing and optimality criteria with weight-strength and other so-called engineering methods. Applications of this approach to aviation structures are discussed with a detailed description of how the total problem of structural sizing can be broken down into subproblems for best utilization of each algorithm and for efficient organization of the program into iterative loops. Typical results are examined for a number of examples.

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.

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.

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

NASA Astrophysics Data System (ADS)

Gorelick, Steven M.; Voss, Clifford I.; Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H.

1984-04-01

A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. Restrictions can be placed on hydraulic heads, stresses, and gradients, in addition to contaminant concentrations and fluxes. These restrictions can be distributed over space and time. Three design strategies are demonstrated for an aquifer that is polluted by a constant contaminant source: they are pumping for contaminant removal, water injection for in-ground dilution, and a pumping, treatment, and injection cycle. A transient model designs either contaminant plume interception or in-ground dilution so that water quality standards are met. The method is not limited to these cases. It is generally applicable to the optimization of many types of distributed parameter systems.

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.

Direct Method Transcription for a Human-Class Translunar Injection Trajectory Optimization

NASA Technical Reports Server (NTRS)

Witzberger, Kevin E.; Zeiler, Tom

2012-01-01

This paper presents a new trajectory optimization software package developed in the framework of a low-to-high fidelity 3 degrees-of-freedom (DOF)/6-DOF vehicle simulation program named Mission Analysis Simulation Tool in Fortran (MASTIF) and its application to a translunar trajectory optimization problem. The functionality of the developed optimization package is implemented as a new "mode" in generalized settings to make it applicable for a general trajectory optimization problem. In doing so, a direct optimization method using collocation is employed for solving the problem. Trajectory optimization problems in MASTIF are transcribed to a constrained nonlinear programming (NLP) problem and solved with SNOPT, a commercially available NLP solver. A detailed description of the optimization software developed is provided as well as the transcription specifics for the translunar injection (TLI) problem. The analysis includes a 3-DOF trajectory TLI optimization and a 3-DOF vehicle TLI simulation using closed-loop guidance.

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

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

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.

The forest and agricultural sector optimization model (FASOM): model structure and policy applications.

Treesearch

Darius M. Adams; Ralph J. Alig; J.M. Callaway; Bruce A. McCarl; Steven M. Winnett

1996-01-01

The Forest and Agricultural Sector Optimization Model (FASOM) is a dynamic, nonlinear programming model of the forest and agricultural sectors in the United States. The FASOM model initially was developed to evaluate welfare and market impacts of alternative policies for sequestering carbon in trees but also has been applied to a wider range of forest and agricultural...

A technique for locating function roots and for satisfying equality constraints in optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw

1991-01-01

A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.

A technique for locating function roots and for satisfying equality constraints in optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.

1992-01-01

A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.

Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

PubMed

Lee, Chang Jun

2015-01-01

In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

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

PubMed

Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

2016-09-01

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

Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming

NASA Astrophysics Data System (ADS)

Hubicki, Christian; Goldman, Daniel; Ames, Aaron

In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Fuzzy physical programming for Space Manoeuvre Vehicles trajectory optimization based on hp-adaptive pseudospectral method

NASA Astrophysics Data System (ADS)

Chai, Runqi; Savvaris, Al; Tsourdos, Antonios

2016-06-01

In this paper, a fuzzy physical programming (FPP) method has been introduced for solving multi-objective Space Manoeuvre Vehicles (SMV) skip trajectory optimization problem based on hp-adaptive pseudospectral methods. The dynamic model of SMV is elaborated and then, by employing hp-adaptive pseudospectral methods, the problem has been transformed to nonlinear programming (NLP) problem. According to the mission requirements, the solutions were calculated for each single-objective scenario. To get a compromised solution for each target, the fuzzy physical programming (FPP) model is proposed. The preference function is established with considering the fuzzy factor of the system such that a proper compromised trajectory can be acquired. In addition, the NSGA-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the FPP solution. Simulation results indicate that the proposed method is effective and feasible in terms of dealing with the multi-objective skip trajectory optimization for the SMV.

Topology-changing shape optimization with the genetic algorithm

NASA Astrophysics Data System (ADS)

Lamberson, Steven E., Jr.

The goal is to take a traditional shape optimization problem statement and modify it slightly to allow for prescribed changes in topology. This modification enables greater flexibility in the choice of parameters for the topology optimization problem, while improving the direct physical relevance of the results. This modification involves changing the optimization problem statement from a nonlinear programming problem into a form of mixed-discrete nonlinear programing problem. The present work demonstrates one possible way of using the Genetic Algorithm (GA) to solve such a problem, including the use of "masking bits" and a new modification to the bit-string affinity (BSA) termination criterion specifically designed for problems with "masking bits." A simple ten-bar truss problem proves the utility of the modified BSA for this type of problem. A more complicated two dimensional bracket problem is solved using both the proposed approach and a more traditional topology optimization approach (Solid Isotropic Microstructure with Penalization or SIMP) to enable comparison. The proposed approach is able to solve problems with both local and global constraints, which is something traditional methods cannot do. The proposed approach has a significantly higher computational burden --- on the order of 100 times larger than SIMP, although the proposed approach is able to offset this with parallel computing.

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

PubMed

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

2011-12-01

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

A study of the use of linear programming techniques to improve the performance in design optimization problems

NASA Technical Reports Server (NTRS)

Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw

1988-01-01

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

Optimal planning of co-firing alternative fuels with coal in a power plant by grey nonlinear mixed integer programming model.

PubMed

Ko, Andi Setiady; Chang, Ni-Bin

2008-07-01

Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time.

Fitting Nonlinear Curves by use of Optimization Techniques

NASA Technical Reports Server (NTRS)

Hill, Scott A.

2005-01-01

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Supersonic Aerodynamic Design Improvements of an Arrow-Wing HSCT Configuration Using Nonlinear Point Design Methods

NASA Technical Reports Server (NTRS)

Unger, Eric R.; Hager, James O.; Agrawal, Shreekant

1999-01-01

This paper is a discussion of the supersonic nonlinear point design optimization efforts at McDonnell Douglas Aerospace under the High-Speed Research (HSR) program. The baseline for these optimization efforts has been the M2.4-7A configuration which represents an arrow-wing technology for the High-Speed Civil Transport (HSCT). Optimization work on this configuration began in early 1994 and continued into 1996. Initial work focused on optimization of the wing camber and twist on a wing/body configuration and reductions of 3.5 drag counts (Euler) were realized. The next phase of the optimization effort included fuselage camber along with the wing and a drag reduction of 5.0 counts was achieved. Including the effects of the nacelles and diverters into the optimization problem became the next focus where a reduction of 6.6 counts (Euler W/B/N/D) was eventually realized. The final two phases of the effort included a large set of constraints designed to make the final optimized configuration more realistic and they were successful albeit with a loss of performance.

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.« less

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.

Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming

PubMed Central

Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias

2012-01-01

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398

Analysis of decision support system for dredging operations management.

DOT National Transportation Integrated Search

2005-12-01

This research developed an improved method for optimizing the disposal of dredged material : at offshore disposal sites. A nonlinear programming model has been developed to assist in : the development of dredging plans at open water disposal sites. T...

Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method

NASA Astrophysics Data System (ADS)

Li, Jing

2016-07-01

This paper investigates fuel-optimal low-thrust formation reconfiguration near circular orbit. Based on the Clohessy-Wiltshire equations, first-order necessary optimality conditions are derived from the Pontryagin's maximum principle. The fuel-optimal impulsive solution is utilized to divide the low-thrust trajectory into thrust and coast arcs. By introducing the switching times as optimization variables, the fuel-optimal low-thrust formation reconfiguration is posed as a nonlinear programming problem (NLP) via direct transcription using multiple-phase Radau pseudospectral method (RPM), which is then solved by a sparse nonlinear optimization software SNOPT. To facilitate optimality verification and, if necessary, further refinement of the optimized solution of the NLP, formulas for mass costate estimation and initial costates scaling are presented. Numerical examples are given to show the application of the proposed optimization method. To fix the problem, generic fuel-optimal low-thrust formation reconfiguration can be simplified as reconfiguration without any initial and terminal coast arcs, whose optimal solutions can be efficiently obtained from the multiple-phase RPM at the cost of a slight fuel increment. Finally, influence of the specific impulse and maximum thrust magnitude on the fuel-optimal low-thrust formation reconfiguration is analyzed. Numerical results shown the links and differences between the fuel-optimal impulsive and low-thrust solutions.

Nonlinear programming for classification problems in machine learning

NASA Astrophysics Data System (ADS)

Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio

2016-10-01

We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted

1990-01-01

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Explicit time integration of finite element models on a vectorized, concurrent computer with shared memory

NASA Technical Reports Server (NTRS)

Gilbertsen, Noreen D.; Belytschko, Ted

1990-01-01

The implementation of a nonlinear explicit program on a vectorized, concurrent computer with shared memory is described and studied. The conflict between vectorization and concurrency is described and some guidelines are given for optimal block sizes. Several example problems are summarized to illustrate the types of speed-ups which can be achieved by reprogramming as compared to compiler optimization.

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

The Krigifier: A Procedure for Generating Pseudorandom Nonlinear Objective Functions for Computational Experimentation

NASA Technical Reports Server (NTRS)

Trosset, Michael W.

1999-01-01

Comprehensive computational experiments to assess the performance of algorithms for numerical optimization require (among other things) a practical procedure for generating pseudorandom nonlinear objective functions. We propose a procedure that is based on the convenient fiction that objective functions are realizations of stochastic processes. This report details the calculations necessary to implement our procedure for the case of certain stationary Gaussian processes and presents a specific implementation in the statistical programming language S-PLUS.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

River water quality management considering agricultural return flows: application of a nonlinear two-stage stochastic fuzzy programming.

PubMed

Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam

2015-04-01

In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.

DAKOTA Design Analysis Kit for Optimization and Terascale

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

Adams, Brian M.; Dalbey, Keith R.; Eldred, Michael S.

2010-02-24

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes (computational models) and iterative analysis methods. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and analysis of computational models on high performance computers.A user provides a set of DAKOTA commands in an input file and launches DAKOTA. DAKOTA invokes instances of the computational models, collects their results, and performs systems analyses. DAKOTA contains algorithms for optimization with gradient and nongradient-basedmore » methods; uncertainty quantification with sampling, reliability, polynomial chaos, stochastic collocation, and epistemic methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as hybrid optimization, surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. Services for parallel computing, simulation interfacing, approximation modeling, fault tolerance, restart, and graphics are also included.« less

Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design

NASA Technical Reports Server (NTRS)

Sims, Jon A.; Finlayson, Paul A.; Rinderle, Edward A.; Vavrina, Matthew A.; Kowalkowski, Theresa D.

2006-01-01

A tool developed for the preliminary design of low-thrust trajectories is described. The trajectory is discretized into segments and a nonlinear programming method is used for optimization. The tool is easy to use, has robust convergence, and can handle many intermediate encounters. In addition, the tool has a wide variety of features, including several options for objective function and different low-thrust propulsion models (e.g., solar electric propulsion, nuclear electric propulsion, and solar sail). High-thrust, impulsive trajectories can also be optimized.

On unified modeling, theory, and method for solving multi-scale global optimization problems

NASA Astrophysics Data System (ADS)

Gao, David Yang

2016-10-01

A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.

Comparison of some optimal control methods for the design of turbine blades

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Grant, G. N. C.

1977-01-01

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

DE and NLP Based QPLS Algorithm

NASA Astrophysics Data System (ADS)

Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo

As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

NASA Astrophysics Data System (ADS)

Kendrick, Rachel

Intensity-modulated radiation therapy is used to better conform the radiation dose to the target, which includes avoiding healthy tissue. Planning programs employ optimization methods to search for the best fluence of each photon beam, and therefore to create the best treatment plan. The Computational Environment for Radiotherapy Research (CERR), a program written in MATLAB, was used to examine some commonly-used algorithms for one 5-beam plan. Algorithms include the genetic algorithm, quadratic programming, pattern search, constrained nonlinear optimization, simulated annealing, the optimization method used in Varian EclipseTM, and some hybrids of these. Quadratic programing, simulated annealing, and a quadratic/simulated annealing hybrid were also separately compared using different prescription doses. The results of each dose-volume histogram as well as the visual dose color wash were used to compare the plans. CERR's built-in quadratic programming provided the best overall plan, but avoidance of the organ-at-risk was rivaled by other programs. Hybrids of quadratic programming with some of these algorithms seems to suggest the possibility of better planning programs, as shown by the improved quadratic/simulated annealing plan when compared to the simulated annealing algorithm alone. Further experimentation will be done to improve cost functions and computational time.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

Optimizing Force Deployment and Force Structure for the Rapid Deployment Force

DTIC Science & Technology

1984-03-01

Analysis . . . . .. .. ... ... 97 Experimental Design . . . . . .. .. .. ... 99 IX. Use of a Flexible Response Surface ........ 10.2 Selection of a...setS . ere designe . arun, programming methodology , where the require: s.stem re..r is input and the model optimizes the num=er. :::pe, cargo. an...to obtain new computer outputs" (Ref 38:23). The methodology can be used with any decision model, linear or nonlinear. Experimental Desion Since the

SPX: The Tenth International Conference on Stochastic Programming

DTIC Science & Technology

2004-10-01

On structuring energy contract portfolios in competitive markets . Antonio Alonso-Ayuso, Universidad Rey Juan Carlos. (p. 28) 2. Mean-risk optimization ...ThA 8:00-9:30 Ballroom South: Portfolio Optimization Chair: Gerd Infanger, Stanford University 1. The impact of serial correlation of returns on ... the L-shaped method is to approximate the non-linear penalty term in the objective by a linear one . We use the implicit LX

Real-time trajectory optimization on parallel processors

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1993-01-01

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

An intuitionistic fuzzy multi-objective non-linear programming model for sustainable irrigation water allocation under the combination of dry and wet conditions

NASA Astrophysics Data System (ADS)

Li, Mo; Fu, Qiang; Singh, Vijay P.; Ma, Mingwei; Liu, Xiao

2017-12-01

Water scarcity causes conflicts among natural resources, society and economy and reinforces the need for optimal allocation of irrigation water resources in a sustainable way. Uncertainties caused by natural conditions and human activities make optimal allocation more complex. An intuitionistic fuzzy multi-objective non-linear programming (IFMONLP) model for irrigation water allocation under the combination of dry and wet conditions is developed to help decision makers mitigate water scarcity. The model is capable of quantitatively solving multiple problems including crop yield increase, blue water saving, and water supply cost reduction to obtain a balanced water allocation scheme using a multi-objective non-linear programming technique. Moreover, it can deal with uncertainty as well as hesitation based on the introduction of intuitionistic fuzzy numbers. Consideration of the combination of dry and wet conditions for water availability and precipitation makes it possible to gain insights into the various irrigation water allocations, and joint probabilities based on copula functions provide decision makers an average standard for irrigation. A case study on optimally allocating both surface water and groundwater to different growth periods of rice in different subareas in Heping irrigation area, Qing'an County, northeast China shows the potential and applicability of the developed model. Results show that the crop yield increase target especially in tillering and elongation stages is a prevailing concern when more water is available, and trading schemes can mitigate water supply cost and save water with an increased grain output. Results also reveal that the water allocation schemes are sensitive to the variation of water availability and precipitation with uncertain characteristics. The IFMONLP model is applicable for most irrigation areas with limited water supplies to determine irrigation water strategies under a fuzzy environment.

Optimization of neural network architecture using genetic programming improves detection and modeling of gene-gene interactions in studies of human diseases

PubMed Central

Ritchie, Marylyn D; White, Bill C; Parker, Joel S; Hahn, Lance W; Moore, Jason H

2003-01-01

Background Appropriate definition of neural network architecture prior to data analysis is crucial for successful data mining. This can be challenging when the underlying model of the data is unknown. The goal of this study was to determine whether optimizing neural network architecture using genetic programming as a machine learning strategy would improve the ability of neural networks to model and detect nonlinear interactions among genes in studies of common human diseases. Results Using simulated data, we show that a genetic programming optimized neural network approach is able to model gene-gene interactions as well as a traditional back propagation neural network. Furthermore, the genetic programming optimized neural network is better than the traditional back propagation neural network approach in terms of predictive ability and power to detect gene-gene interactions when non-functional polymorphisms are present. Conclusion This study suggests that a machine learning strategy for optimizing neural network architecture may be preferable to traditional trial-and-error approaches for the identification and characterization of gene-gene interactions in common, complex human diseases. PMID:12846935

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

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

PubMed

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

2017-10-01

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

Optimal Frequency-Domain System Realization with Weighting

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Maghami, Peiman G.

1999-01-01

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation uses a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. Three different approaches are introduced to fine-tune the model using nonlinear programming methods to minimize the desired cost function. The first method uses an eigenvalue assignment technique to reassign a subset of system poles to improve the identified model. The second method deals with the model in the real Schur or modal form, reassigns a subset of system poles, and adjusts the columns (rows) of the input (output) influence matrix using a nonlinear optimizer. The third method also optimizes a subset of poles, but the input and output influence matrices are refined at every optimization step through least-squares procedures.

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.

Global optimization algorithm for heat exchanger networks

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

Quesada, I.; Grossmann, I.E.

This paper deals with the global optimization of heat exchanger networks with fixed topology. It is shown that if linear area cost functions are assumed, as well as arithmetic mean driving force temperature differences in networks with isothermal mixing, the corresponding nonlinear programming (NLP) optimization problem involves linear constraints and a sum of linear fractional functions in the objective which are nonconvex. A rigorous algorithm is proposed that is based on a convex NLP underestimator that involves linear and nonlinear estimators for fractional and bilinear terms which provide a tight lower bound to the global optimum. This NLP problem ismore » used within a spatial branch and bound method for which branching rules are given. Basic properties of the proposed method are presented, and its application is illustrated with several example problems. The results show that the proposed method only requires few nodes in the branch and bound search.« less

New Mathematical Strategy Using Branch and Bound Method

NASA Astrophysics Data System (ADS)

Tarray, Tanveer Ahmad; Bhat, Muzafar Rasool

In this paper, the problem of optimal allocation in stratified random sampling is used in the presence of nonresponse. The problem is formulated as a nonlinear programming problem (NLPP) and is solved using Branch and Bound method. Also the results are formulated through LINGO.

Vibrational spectroscopic and non-linear optical activity studies on nicotinanilide : A DFT approach

NASA Astrophysics Data System (ADS)

Premkumar, S.; Jawahar, A.; Mathavan, T.; Dhas, M. Kumara; Benial, A. Milton Franklin

2015-06-01

The molecular structure of nicotinanilide was optimized by the DFT/B3LYP method with cc-pVTZ basis set using Gaussian 09 program. The first order hyperpolarizability of the molecule was calculated, which exhibits the higher nonlinear optical activity. The natural bond orbital analysis confirms the presence of intramolecular charge transfer and the hydrogen bonding interaction, which leads to the higher nonlinear optical activity of the molecule. The Frontier molecular orbitals analysis of the molecule shows that the delocalization of electron density occurs within the molecule. The lower energy gap indicates that the hydrogen bond formation between the charged species. The vibrational frequencies were calculated and assigned on the basis of potential energy distribution calculation using the VEDA 4.0 program and the corresponding vibrational spectra were simulated. Hence, the nicotinanilide molecule can be a good candidate for second-order NLO material.

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.

Optimal wide-area monitoring and nonlinear adaptive coordinating neurocontrol of a power system with wind power integration and multiple FACTS devices.

PubMed

Qiao, Wei; Venayagamoorthy, Ganesh K; Harley, Ronald G

2008-01-01

Wide-area coordinating control is becoming an important issue and a challenging problem in the power industry. This paper proposes a novel optimal wide-area coordinating neurocontrol (WACNC), based on wide-area measurements, for a power system with power system stabilizers, a large wind farm and multiple flexible ac transmission system (FACTS) devices. An optimal wide-area monitor (OWAM), which is a radial basis function neural network (RBFNN), is designed to identify the input-output dynamics of the nonlinear power system. Its parameters are optimized through particle swarm optimization (PSO). Based on the OWAM, the WACNC is then designed by using the dual heuristic programming (DHP) method and RBFNNs, while considering the effect of signal transmission delays. The WACNC operates at a global level to coordinate the actions of local power system controllers. Each local controller communicates with the WACNC, receives remote control signals from the WACNC to enhance its dynamic performance and therefore helps improve system-wide dynamic and transient performance. The proposed control is verified by simulation studies on a multimachine power system.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Luy, N. T.

2018-04-01

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

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.

Synthesizing optimal waste blends

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

Narayan, V.; Diwekar, W.M.; Hoza, M.

Vitrification of tank wastes to form glass is a technique that will be used for the disposal of high-level waste at Hanford. Process and storage economics show that minimizing the total number of glass logs produced is the key to keeping cost as low as possible. The amount of glass produced can be reduced by blending of the wastes. The optimal way to combine the tanks to minimize the vole of glass can be determined from a discrete blend calculation. However, this problem results in a combinatorial explosion as the number of tanks increases. Moreover, the property constraints make thismore » problem highly nonconvex where many algorithms get trapped in local minima. In this paper the authors examine the use of different combinatorial optimization approaches to solve this problem. A two-stage approach using a combination of simulated annealing and nonlinear programming (NLP) is developed. The results of different methods such as the heuristics approach based on human knowledge and judgment, the mixed integer nonlinear programming (MINLP) approach with GAMS, and branch and bound with lower bound derived from the structure of the given blending problem are compared with this coupled simulated annealing and NLP approach.« less

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

Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

NASA Astrophysics Data System (ADS)

Chen, Wei

2015-07-01

In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

Optimal Mixing On The Sphere

DTIC Science & Technology

2010-11-10

CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ...ORGANIZATION NAME(S) AND ADDRESS(ES) Woods Hole Oceanographic Institution,Woods Hole,MA,02543 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING...consider an alternate means of finding the minima of 〈|θ|2〉. We perform a two-part optimization process based on Matlab’s built-in nonlinear

Investigation on application of genetic algorithms to optimal reactive power dispatch of power systems

NASA Astrophysics Data System (ADS)

Wu, Q. H.; Ma, J. T.

1993-09-01

A primary investigation into application of genetic algorithms in optimal reactive power dispatch and voltage control is presented. The application was achieved, based on (the United Kingdom) National Grid 48 bus network model, using a novel genetic search approach. Simulation results, compared with that obtained using nonlinear programming methods, are included to show the potential of applications of the genetic search methodology in power system economical and secure operations.

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

NASA Technical Reports Server (NTRS)

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

1996-01-01

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Performance Trend of Different Algorithms for Structural Design Optimization

NASA Technical Reports Server (NTRS)

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

1996-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Research on design method of the full form ship with minimum thrust deduction factor

NASA Astrophysics Data System (ADS)

Zhang, Bao-ji; Miao, Ai-qin; Zhang, Zhu-xin

2015-04-01

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique (SUMT) interior point method of Nonlinear Programming (NLP) was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

Evolutionary and biological metaphors for engineering design

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

Jakiela, M.

1994-12-31

Since computing became generally available, there has been strong interest in using computers to assist and automate engineering design processes. Specifically, for design optimization and automation, nonlinear programming and artificial intelligence techniques have been extensively studied. New computational techniques, based upon the natural processes of evolution, adaptation, and learing, are showing promise because of their generality and robustness. This presentation will describe the use of two such techniques, genetic algorithms and classifier systems, for a variety of engineering design problems. Structural topology optimization, meshing, and general engineering optimization are shown as example applications.

An optimal system design process for a Mars roving vehicle

NASA Technical Reports Server (NTRS)

Pavarini, C.; Baker, J.; Goldberg, A.

1971-01-01

The problem of determining the optimal design for a Mars roving vehicle is considered. A system model is generated by consideration of the physical constraints on the design parameters and the requirement that the system be deliverable to the Mars surface. An expression which evaluates system performance relative to mission goals as a function of the design parameters only is developed. The use of nonlinear programming techniques to optimize the design is proposed and an example considering only two of the vehicle subsystems is formulated and solved.

Optimal reconfiguration strategy for a degradable multimodule computing system

NASA Technical Reports Server (NTRS)

Lee, Yann-Hang; Shin, Kang G.

1987-01-01

The present quantitative approach to the problem of reconfiguring a degradable multimode system assigns some modules to computation and arranges others for reliability. By using expected total reward as the optimal criterion, there emerges an active reconfiguration strategy based not only on the occurrence of failure but the progression of the given mission. This reconfiguration strategy requires specification of the times at which the system should undergo reconfiguration, and the configurations to which the system should change. The optimal reconfiguration problem is converted to integer nonlinear knapsack and fractional programming problems.

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

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

Sun, Y.; Borland, Michael

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

A holistic approach to movement education in sport and fitness: a systems based model.

PubMed

Polsgrove, Myles Jay

2012-01-01

The typical model used by movement professionals to enhance performance relies on the notion that a linear increase in load results in steady and progressive gains, whereby, the greater the effort, the greater the gains in performance. Traditional approaches to movement progression typically rely on the proper sequencing of extrinsically based activities to facilitate the individual in reaching performance objectives. However, physical rehabilitation or physical performance rarely progresses in such a linear fashion; instead they tend to evolve non-linearly and rather unpredictably. A dynamic system can be described as an entity that self-organizes into increasingly complex forms. Applying this view to the human body, practitioners could facilitate non-linear performance gains through a systems based programming approach. Utilizing a dynamic systems view, the Holistic Approach to Movement Education (HADME) is a model designed to optimize performance by accounting for non-linear and self-organizing traits associated with human movement. In this model, gains in performance occur through advancing individual perspectives and through optimizing sub-system performance. This inward shift of the focus of performance creates a sharper self-awareness and may lead to more optimal movements. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

Automated design and optimization of flexible booster autopilots via linear programming, volume 1

NASA Technical Reports Server (NTRS)

Hauser, F. D.

1972-01-01

A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory dispersions; and (3) stability with specified tolerances on the vehicle and flight control system parameters. The method is applicable to very high order systems (30th and greater per flight condition). Examples are provided that demonstrate the successful application of the employed algorithm to the design of autopilots for both single and multiple flight conditions.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

High-performance image reconstruction in fluorescence tomography on desktop computers and graphics hardware.

PubMed

Freiberger, Manuel; Egger, Herbert; Liebmann, Manfred; Scharfetter, Hermann

2011-11-01

Image reconstruction in fluorescence optical tomography is a three-dimensional nonlinear ill-posed problem governed by a system of partial differential equations. In this paper we demonstrate that a combination of state of the art numerical algorithms and a careful hardware optimized implementation allows to solve this large-scale inverse problem in a few seconds on standard desktop PCs with modern graphics hardware. In particular, we present methods to solve not only the forward but also the non-linear inverse problem by massively parallel programming on graphics processors. A comparison of optimized CPU and GPU implementations shows that the reconstruction can be accelerated by factors of about 15 through the use of the graphics hardware without compromising the accuracy in the reconstructed images.

Local structure of equality constrained NLP problems

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

Mari, J.

We show that locally around a feasible point, the behavior of an equality constrained nonlinear program is described by the gradient and the Hessian of the Lagrangian on the tangent subspace. In particular this holds true for reduced gradient approaches. Applying the same ideas to the control of nonlinear ODE:s, one can device first and second order methods that can be applied also to stiff problems. We finally describe an application of these ideas to the optimization of the production of human growth factor by fed-batch fermentation.

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

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2016-01-01

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

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

A Multiobjective Interval Programming Model for Wind-Hydrothermal Power System Dispatching Using 2-Step Optimization Algorithm

PubMed Central

Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision. PMID:24895663

A multiobjective interval programming model for wind-hydrothermal power system dispatching using 2-step optimization algorithm.

PubMed

Ren, Kun; Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.

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.

Optimization techniques applied to spectrum management for communications satellites

NASA Astrophysics Data System (ADS)

Ottey, H. R.; Sullivan, T. M.; Zusman, F. S.

This paper describes user requirements, algorithms and software design features for the application of optimization techniques to the management of the geostationary orbit/spectrum resource. Relevant problems include parameter sensitivity analyses, frequency and orbit position assignment coordination, and orbit position allotment planning. It is shown how integer and nonlinear programming as well as heuristic search techniques can be used to solve these problems. Formalized mathematical objective functions that define the problems are presented. Constraint functions that impart the necessary solution bounds are described. A versatile program structure is outlined, which would allow problems to be solved in stages while varying the problem space, solution resolution, objective function and constraints.

Optimization model of vaccination strategy for dengue transmission

NASA Astrophysics Data System (ADS)

Widayani, H.; Kallista, M.; Nuraini, N.; Sari, M. Y.

2014-02-01

Dengue fever is emerging tropical and subtropical disease caused by dengue virus infection. The vaccination should be done as a prevention of epidemic in population. The host-vector model are modified with consider a vaccination factor to prevent the occurrence of epidemic dengue in a population. An optimal vaccination strategy using non-linear objective function was proposed. The genetic algorithm programming techniques are combined with fourth-order Runge-Kutta method to construct the optimal vaccination. In this paper, the appropriate vaccination strategy by using the optimal minimum cost function which can reduce the number of epidemic was analyzed. The numerical simulation for some specific cases of vaccination strategy is shown.

Neural dynamic optimization for control systems. I. Background.

PubMed

Seong, C Y; Widrow, B

2001-01-01

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

Neural dynamic optimization for control systems.III. Applications.

PubMed

Seong, C Y; Widrow, B

2001-01-01

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

Neural dynamic optimization for control systems.II. Theory.

PubMed

Seong, C Y; Widrow, B

2001-01-01

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

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.

Experiences at Langley Research Center in the application of optimization techniques to helicopter airframes for vibration reduction

NASA Technical Reports Server (NTRS)

Murthy, T. Sreekanta; Kvaternik, Raymond G.

1991-01-01

A NASA/industry rotorcraft structural dynamics program known as Design Analysis Methods for VIBrationS (DAMVIBS) was initiated at Langley Research Center in 1984 with the objective of establishing the technology base needed by the industry for developing an advanced finite-element-based vibrations design analysis capability for airframe structures. As a part of the in-house activities contributing to that program, a study was undertaken to investigate the use of formal, nonlinear programming-based, numerical optimization techniques for airframe vibrations design work. Considerable progress has been made in connection with that study since its inception in 1985. This paper presents a unified summary of the experiences and results of that study. The formulation and solution of airframe optimization problems are discussed. Particular attention is given to describing the implementation of a new computational procedure based on MSC/NASTRAN and CONstrained function MINimization (CONMIN) in a computer program system called DYNOPT for the optimization of airframes subject to strength, frequency, dynamic response, and fatigue constraints. The results from the application of the DYNOPT program to the Bell AH-1G helicopter are presented and discussed.

Optimum sensitivity derivatives of objective functions in nonlinear programming

NASA Technical Reports Server (NTRS)

Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.

1983-01-01

The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.

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.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

PubMed Central

Naeem, Muhammad; Illanko, Kandasamy; Karmokar, Ashok; Anpalagan, Alagan; Jaseemuddin, Muhammad

2013-01-01

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated. PMID:23966194

Algorithmic Perspectives on Problem Formulations in MDO

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia M.; Lewis, Robert Michael

2000-01-01

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

A new numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

PubMed

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

2016-01-01

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.

Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints

NASA Technical Reports Server (NTRS)

Patnaik, Surya; Gendy, Atef; Berke, Laszlo; Hopkins, Dale

1997-01-01

The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples.

Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.

PubMed

Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello

2007-01-01

A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.

Aerospace Structures Design on Computers

DTIC Science & Technology

1989-03-01

loud or lter’itr- strm C M~eort load or mex~murn load AMeon strews o,. strvss (Q) hm’nur loS1 (b) me -im (a) Fluctuating tension load cycle; (b...constraint deletion techniques in the struc- tural applications of nonlinear programming algorithms. The way this concept is used in the optimality criteria

Vibrational spectroscopic, structural and nonlinear optical activity studies on 6-aminonicotinamide: A DFT approach

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

Asath, R. Mohamed; Premkumar, S.; Mathavan, T.

2016-05-23

The conformational analysis was carried out for 6-aminonicotinamide (ANA) using potential energy surface scan method and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the related molecular properties were calculated. The ultraviolet-visible spectrum was simulated for both in the gas phase andmore » liquid phase (ethanol) and the π to π* electronic transition was predicted. The nonlinear optical (NLO) activity was studied by means of the first order hyperpolarizability value, which was 8.61 times greater than the urea and the natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ANA molecule is a promising candidate for the NLO materials.« less

Vibrational spectroscopic, structural and nonlinear optical activity studies on 2-amino-3-chloro-5-trifluoromethyl pyridine: A DFT approach

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

Asath, R. Mohamed; Premkumar, S.; Mathavan, T.

2016-05-23

The conformational analysis was carried out for 2-amino-3-chloro-5-trifluoromethylpyridine using potential energy surface (PES) scan and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program package. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness of the moleculemore » were carried out. The nonlinear optical (NLO) activity was studied and the first order hyperpolarizability value was computed, which was 3.48 times greater than the urea. The natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ACTP molecule is a promising candidate for NLO materials.« less

Vibrational spectroscopic, structural and nonlinear optical activity studies on 6-aminonicotinamide: A DFT approach

NASA Astrophysics Data System (ADS)

Asath, R. Mohamed; Premkumar, S.; Rekha, T. N.; Jawahar, A.; Mathavan, T.; Benial, A. Milton Franklin

2016-05-01

The conformational analysis was carried out for 6-aminonicotinamide (ANA) using potential energy surface scan method and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the related molecular properties were calculated. The ultraviolet-visible spectrum was simulated for both in the gas phase and liquid phase (ethanol) and the л to л* electronic transition was predicted. The nonlinear optical (NLO) activity was studied by means of the first order hyperpolarizability value, which was 8.61 times greater than the urea and the natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ANA molecule is a promising candidate for the NLO materials.

Vibrational spectroscopic, structural and nonlinear optical activity studies on 2-amino-3-chloro-5-trifluoromethyl pyridine: A DFT approach

NASA Astrophysics Data System (ADS)

Asath, R. Mohamed; Premkumar, S.; Rekha, T. N.; Jawahar, A.; Mathavan, T.; Benial, A. Milton Franklin

2016-05-01

The conformational analysis was carried out for 2-amino-3-chloro-5-trifluoromethylpyridine using potential energy surface (PES) scan and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program package. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness of the molecule were carried out. The nonlinear optical (NLO) activity was studied and the first order hyperpolarizability value was computed, which was 3.48 times greater than the urea. The natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ACTP molecule is a promising candidate for NLO materials.

Conformational, vibrational spectroscopic and nonlinear optical activity studies on N,N-Di-Boc-2-amino pyridine : A DFT approach

NASA Astrophysics Data System (ADS)

Asath, R. Mohamed; Premkumar, R.; Mathavan, T.; Benial, A. Milton Franklin

2017-05-01

The conformational analysis was carried out for N,N-Di-Boc-2-amino pyridine using potential energy surface (PES) scan and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVTZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program package. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness of the molecule were carried out. The nonlinear optical (NLO) activity was examined and the first order hyperpolarizability value was computed, which was 2.27 times greater than the urea. The natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the DBAP molecule is a promising candidate for NLO materials.

On the utilization of engineering knowledge in design optimization

NASA Technical Reports Server (NTRS)

Papalambros, P.

1984-01-01

Some current research work conducted at the University of Michigan is described to illustrate efforts for incorporating knowledge in optimization in a nontraditional way. The incorporation of available knowledge in a logic structure is examined in two circumstances. The first examines the possibility of introducing global design information in a local active set strategy implemented during the iterations of projection-type algorithms for nonlinearly constrained problems. The technique used algorithms for nonlinearly constrained problems. The technique used combines global and local monotinicity analysis of the objective and constraint functions. The second examines a knowledge-based program which aids the user to create condigurations that are most desirable from the manufacturing assembly viewpoint. The data bank used is the classification scheme suggested by Boothroyd. The important aspect of this program is that it is an aid for synthesis intended for use in the design concept phase in a way similar to the so-called idea-triggers in creativity-enhancement techniques like brain-storming. The idea generation, however, is not random but it is driven by the goal of achieving the best acceptable configuration.

Application of decomposition techniques to the preliminary design of a transport aircraft

NASA Technical Reports Server (NTRS)

Rogan, J. E.; Kolb, M. A.

1987-01-01

A nonlinear constrained optimization problem describing the preliminary design process for a transport aircraft has been formulated. A multifaceted decomposition of the optimization problem has been made. Flight dynamics, flexible aircraft loads and deformations, and preliminary structural design subproblems appear prominently in the decomposition. The use of design process decomposition for scheduling design projects, a new system integration approach to configuration control, and the application of object-centered programming to a new generation of design tools are discussed.

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

PubMed

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

2017-07-01

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

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

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

A reduced successive quadratic programming strategy for errors-in-variables estimation.

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

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.« less

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

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

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

DOE PAGES

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.; ...

2017-05-08

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

An integrated simulation and optimization approach for managing human health risks of atmospheric pollutants by coal-fired power plants.

PubMed

Dai, C; Cai, X H; Cai, Y P; Guo, H C; Sun, W; Tan, Q; Huang, G H

2014-06-01

This research developed a simulation-aided nonlinear programming model (SNPM). This model incorporated the consideration of pollutant dispersion modeling, and the management of coal blending and the related human health risks within a general modeling framework In SNPM, the simulation effort (i.e., California puff [CALPUFF]) was used to forecast the fate of air pollutants for quantifying the health risk under various conditions, while the optimization studies were to identify the optimal coal blending strategies from a number of alternatives. To solve the model, a surrogate-based indirect search approach was proposed, where the support vector regression (SVR) was used to create a set of easy-to-use and rapid-response surrogates for identifying the function relationships between coal-blending operating conditions and health risks. Through replacing the CALPUFF and the corresponding hazard quotient equation with the surrogates, the computation efficiency could be improved. The developed SNPM was applied to minimize the human health risk associated with air pollutants discharged from Gaojing and Shijingshan power plants in the west of Beijing. Solution results indicated that it could be used for reducing the health risk of the public in the vicinity of the two power plants, identifying desired coal blending strategies for decision makers, and considering a proper balance between coal purchase cost and human health risk. A simulation-aided nonlinear programming model (SNPM) is developed. It integrates the advantages of CALPUFF and nonlinear programming model. To solve the model, a surrogate-based indirect search approach based on the combination of support vector regression and genetic algorithm is proposed. SNPM is applied to reduce the health risk caused by air pollutants discharged from Gaojing and Shijingshan power plants in the west of Beijing. Solution results indicate that it is useful for generating coal blending schemes, reducing the health risk of the public, reflecting the trade-offbetween coal purchase cost and health risk.

Multivariable optimization of liquid rocket engines using particle swarm algorithms

NASA Astrophysics Data System (ADS)

Jones, Daniel Ray

Liquid rocket engines are highly reliable, controllable, and efficient compared to other conventional forms of rocket propulsion. As such, they have seen wide use in the space industry and have become the standard propulsion system for launch vehicles, orbit insertion, and orbital maneuvering. Though these systems are well understood, historical optimization techniques are often inadequate due to the highly non-linear nature of the engine performance problem. In this thesis, a Particle Swarm Optimization (PSO) variant was applied to maximize the specific impulse of a finite-area combustion chamber (FAC) equilibrium flow rocket performance model by controlling the engine's oxidizer-to-fuel ratio and de Laval nozzle expansion and contraction ratios. In addition to the PSO-controlled parameters, engine performance was calculated based on propellant chemistry, combustion chamber pressure, and ambient pressure, which are provided as inputs to the program. The performance code was validated by comparison with NASA's Chemical Equilibrium with Applications (CEA) and the commercially available Rocket Propulsion Analysis (RPA) tool. Similarly, the PSO algorithm was validated by comparison with brute-force optimization, which calculates all possible solutions and subsequently determines which is the optimum. Particle Swarm Optimization was shown to be an effective optimizer capable of quick and reliable convergence for complex functions of multiple non-linear variables.

Optimal satisfaction degree in energy harvesting cognitive radio networks

NASA Astrophysics Data System (ADS)

Li, Zan; Liu, Bo-Yang; Si, Jiang-Bo; Zhou, Fu-Hui

2015-12-01

A cognitive radio (CR) network with energy harvesting (EH) is considered to improve both spectrum efficiency and energy efficiency. A hidden Markov model (HMM) is used to characterize the imperfect spectrum sensing process. In order to maximize the whole satisfaction degree (WSD) of the cognitive radio network, a tradeoff between the average throughput of the secondary user (SU) and the interference to the primary user (PU) is analyzed. We formulate the satisfaction degree optimization problem as a mixed integer nonlinear programming (MINLP) problem. The satisfaction degree optimization problem is solved by using differential evolution (DE) algorithm. The proposed optimization problem allows the network to adaptively achieve the optimal solution based on its required quality of service (Qos). Numerical results are given to verify our analysis. Project supported by the National Natural Science Foundation of China (Grant No. 61301179), the Doctorial Programs Foundation of the Ministry of Education of China (Grant No. 20110203110011), and the 111 Project (Grant No. B08038).

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

A biologically inspired neural network for dynamic programming.

PubMed

Francelin Romero, R A; Kacpryzk, J; Gomide, F

2001-12-01

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.

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

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao

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

Further efforts in optimizing nonlinear optical molecules

NASA Astrophysics Data System (ADS)

Dirk, Carl W.; Caballero, Noel; Tan, Alarice; Kuzyk, Mark G.; Cheng, Lap-Tak A.; Katz, Howard E.; Shilling, Marcia; King, Lori A.

1993-02-01

We summarize some of our past work in the field on optimizing molecules for second order and third order nonlinear optical applications. We also present some previously unpublished results suggesting a particular optimization of the popular cyano- and nitrovinyl acceptor groups. In addition we provide some new quadratic electro-optic results which serve to further verify our choice of a restricted three-level model suitable for optimizing third order nonlinearities in molecules. Finally we present a new squarylium dye with a large third order optical nonlinearity (-9.5 X 10-34 cm7/esu2; EFISH (gamma) at 1906 nm).

Direct Multiple Shooting Optimization with Variable Problem Parameters

NASA Technical Reports Server (NTRS)

Whitley, Ryan J.; Ocampo, Cesar A.

2009-01-01

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

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.

[On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

PubMed

Pasekov, V P

2013-03-01

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

Fuzzy multiobjective models for optimal operation of a hydropower system

NASA Astrophysics Data System (ADS)

Teegavarapu, Ramesh S. V.; Ferreira, André R.; Simonovic, Slobodan P.

2013-06-01

Optimal operation models for a hydropower system using new fuzzy multiobjective mathematical programming models are developed and evaluated in this study. The models use (i) mixed integer nonlinear programming (MINLP) with binary variables and (ii) integrate a new turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream impairment. Reardon method used in solution of genetic algorithm optimization problems forms the basis for development of a new fuzzy multiobjective hydropower system optimization model with creation of Reardon type fuzzy membership functions. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to (i) solve the optimization formulations to avoid computational intractability and combinatorial problems associated with binary variables in unit commitment, (ii) efficiently address Reardon method formulations, and (iii) deal with local optimal solutions obtained from the use of traditional gradient-based solvers. Decision maker's preferences are incorporated within fuzzy mathematical programming formulations to obtain compromise operating rules for a multiobjective reservoir operation problem dominated by conflicting goals of energy production, water quality and conservation releases. Results provide insight into compromise operation rules obtained using the new Reardon fuzzy multiobjective optimization framework and confirm its applicability to a variety of multiobjective water resources problems.

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

Characterizing L1-norm best-fit subspaces

NASA Astrophysics Data System (ADS)

Brooks, J. Paul; Dulá, José H.

2017-05-01

Fitting affine objects to data is the basis of many tools and methodologies in statistics, machine learning, and signal processing. The L1 norm is often employed to produce subspaces exhibiting a robustness to outliers and faulty observations. The L1-norm best-fit subspace problem is directly formulated as a nonlinear, nonconvex, and nondifferentiable optimization problem. The case when the subspace is a hyperplane can be solved to global optimality efficiently by solving a series of linear programs. The problem of finding the best-fit line has recently been shown to be NP-hard. We present necessary conditions for optimality for the best-fit subspace problem, and use them to characterize properties of optimal solutions.

Quantum optimization for training support vector machines.

PubMed

Anguita, Davide; Ridella, Sandro; Rivieccio, Fabio; Zunino, Rodolfo

2003-01-01

Refined concepts, such as Rademacher estimates of model complexity and nonlinear criteria for weighting empirical classification errors, represent recent and promising approaches to characterize the generalization ability of Support Vector Machines (SVMs). The advantages of those techniques lie in both improving the SVM representation ability and yielding tighter generalization bounds. On the other hand, they often make Quadratic-Programming algorithms no longer applicable, and SVM training cannot benefit from efficient, specialized optimization techniques. The paper considers the application of Quantum Computing to solve the problem of effective SVM training, especially in the case of digital implementations. The presented research compares the behavioral aspects of conventional and enhanced SVMs; experiments in both a synthetic and real-world problems support the theoretical analysis. At the same time, the related differences between Quadratic-Programming and Quantum-based optimization techniques are considered.

2D Decision-Making for Multi-Criteria Design Optimization

DTIC Science & Technology

2006-05-01

participating in the same subproblem, information on the tradeoffs between different subproblems is obtained from a sensitivity analysis and used for...accomplished by some other mechanism. For the coordination between subproblem, we use the lexicographical ordering approach for multicriteria ...Sensitivity analysis Our approach uses sensitivity results from nonlinear programming (Fiacco, 1983; Luenberger, 2003), for which we first

A Genetic Algorithm Approach to Nonlinear Least Squares Estimation

ERIC Educational Resources Information Center

Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.

2004-01-01

A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…

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.

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.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

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.

Optimal second order sliding mode control for nonlinear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-07-01

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro

2016-12-01

Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; White, J. A.

1992-01-01

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

2002-01-01

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

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

PubMed

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

2018-05-01

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

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

PubMed

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

2016-08-31

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

Global stability of plane Couette flow beyond the energy stability limit

NASA Astrophysics Data System (ADS)

Fuentes, Federico; Goluskin, David

2017-11-01

This talk will present computations verifying that the laminar state of plane Couette flow is nonlinearly stable to all perturbations. The Reynolds numbers up to which this globally stability is verified are larger than those at which stability can be proven by the energy method, which is the typical method for demonstrating nonlinear stability of a fluid flow. This improvement is achieved by constructing Lyapunov functions that are more general than the energy. These functions are not restricted to being quadratic, and they are allowed to depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal choice of such a Lyapunov function is a convex optimization problem, and it can be constructed with computer assistance by solving a semidefinite program. This general method will be described in a companion talk by David Goluskin; the present talk focuses on its application to plane Couette flow.

Computer Language For Optimization Of Design

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.; Lucas, Stephen H.

1991-01-01

SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

Nonlinear Burn Control and Operating Point Optimization in ITER

NASA Astrophysics Data System (ADS)

Boyer, Mark; Schuster, Eugenio

2013-10-01

Control of the fusion power through regulation of the plasma density and temperature will be essential for achieving and maintaining desired operating points in fusion reactors and burning plasma experiments like ITER. In this work, a volume averaged model for the evolution of the density of energy, deuterium and tritium fuel ions, alpha-particles, and impurity ions is used to synthesize a multi-input multi-output nonlinear feedback controller for stabilizing and modulating the burn condition. Adaptive control techniques are used to account for uncertainty in model parameters, including particle confinement times and recycling rates. The control approach makes use of the different possible methods for altering the fusion power, including adjusting the temperature through auxiliary heating, modulating the density and isotopic mix through fueling, and altering the impurity density through impurity injection. Furthermore, a model-based optimization scheme is proposed to drive the system as close as possible to desired fusion power and temperature references. Constraints are considered in the optimization scheme to ensure that, for example, density and beta limits are avoided, and that optimal operation is achieved even when actuators reach saturation. Supported by the NSF CAREER award program (ECCS-0645086).

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

User's manual for the Macintosh version of PASCO

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Davis, Randall C.

1991-01-01

A user's manual for Macintosh PASCO is presented. Macintosh PASCO is an Apple Macintosh version of PASCO, an existing computer code for structural analysis and optimization of longitudinally stiffened composite panels. PASCO combines a rigorous buckling analysis program with a nonlinear mathematical optimization routine to minimize panel mass. Macintosh PASCO accepts the same input as mainframe versions of PASCO. As output, Macintosh PASCO produces a text file and mode shape plots in the form of Apple Macintosh PICT files. Only the user interface for Macintosh is discussed here.

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.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

An Alternative Approach to the Operation of Multinational Reservoir Systems: Application to the Amistad & Falcon System (Lower Rio Grande/Rí-o Bravo)

NASA Astrophysics Data System (ADS)

Serrat-Capdevila, A.; Valdes, J. B.

2005-12-01

An optimization approach for the operation of international multi-reservoir systems is presented. The approach uses Stochastic Dynamic Programming (SDP) algorithms, both steady-state and real-time, to develop two models. In the first model, the reservoirs and flows of the system are aggregated to yield an equivalent reservoir, and the obtained operating policies are disaggregated using a non-linear optimization procedure for each reservoir and for each nation water balance. In the second model a multi-reservoir approach is applied, disaggregating the releases for each country water share in each reservoir. The non-linear disaggregation algorithm uses SDP-derived operating policies as boundary conditions for a local time-step optimization. Finally, the performance of the different approaches and methods is compared. These models are applied to the Amistad-Falcon International Reservoir System as part of a binational dynamic modeling effort to develop a decision support system tool for a better management of the water resources in the Lower Rio Grande Basin, currently enduring a severe drought.

MONSS: A multi-objective nonlinear simplex search approach

NASA Astrophysics Data System (ADS)

Zapotecas-Martínez, Saúl; Coello Coello, Carlos A.

2016-01-01

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.

Navigation Solution for a Multiple Satellite and Multiple Ground Architecture

DTIC Science & Technology

2014-09-14

Primer Vector Theory . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.6 The Traveling Salesman Problem . . . . . . . . . . . . . . . . . . 12...the Traveling Salesman problem [42]. It is framed as a nonlinear programming, complete combinatorial optimization where the orbital debris pieces relate...impulsive maneuvers and applies his findings to a Hohmann transfer with the addition of mid-course burns and wait times. 2.2.6 The Traveling Salesman

Wind Farm Turbine Type and Placement Optimization

NASA Astrophysics Data System (ADS)

Graf, Peter; Dykes, Katherine; Scott, George; Fields, Jason; Lunacek, Monte; Quick, Julian; Rethore, Pierre-Elouan

2016-09-01

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. This document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Wind farm turbine type and placement optimization

DOE PAGES

Graf, Peter; Dykes, Katherine; Scott, George; ...

2016-10-03

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Travel Demand Modeling

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

Southworth, Frank; Garrow, Dr. Laurie

This chapter describes the principal types of both passenger and freight demand models in use today, providing a brief history of model development supported by references to a number of popular texts on the subject, and directing the reader to papers covering some of the more recent technical developments in the area. Over the past half century a variety of methods have been used to estimate and forecast travel demands, drawing concepts from economic/utility maximization theory, transportation system optimization and spatial interaction theory, using and often combining solution techniques as varied as Box-Jenkins methods, non-linear multivariate regression, non-linear mathematical programming,more » and agent-based microsimulation.« less

The nurse scheduling problem: a goal programming and nonlinear optimization approaches

NASA Astrophysics Data System (ADS)

Hakim, L.; Bakhtiar, T.; Jaharuddin

2017-01-01

Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

A novel technique for optimal integration of active steering and differential braking with estimation to improve vehicle directional stability.

PubMed

Mirzaeinejad, Hossein; Mirzaei, Mehdi; Rafatnia, Sadra

2018-06-11

This study deals with the enhancement of directional stability of vehicle which turns with high speeds on various road conditions using integrated active steering and differential braking systems. In this respect, the minimum usage of intentional asymmetric braking force to compensate the drawbacks of active steering control with small reduction of vehicle longitudinal speed is desired. To this aim, a new optimal multivariable controller is analytically developed for integrated steering and braking systems based on the prediction of vehicle nonlinear responses. A fuzzy programming extracted from the nonlinear phase plane analysis is also used for managing the two control inputs in various driving conditions. With the proposed fuzzy programming, the weight factors of the control inputs are automatically tuned and softly changed. In order to simulate a real-world control system, some required information about the system states and parameters which cannot be directly measured, are estimated using the Unscented Kalman Filter (UKF). Finally, simulations studies are carried out using a validated vehicle model to show the effectiveness of the proposed integrated control system in the presence of model uncertainties and estimation errors. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Multi-objective evolutionary optimization for constructing neural networks for virtual reality visual data mining: application to geophysical prospecting.

PubMed

Valdés, Julio J; Barton, Alan J

2007-05-01

A method for the construction of virtual reality spaces for visual data mining using multi-objective optimization with genetic algorithms on nonlinear discriminant (NDA) neural networks is presented. Two neural network layers (the output and the last hidden) are used for the construction of simultaneous solutions for: (i) a supervised classification of data patterns and (ii) an unsupervised similarity structure preservation between the original data matrix and its image in the new space. A set of spaces are constructed from selected solutions along the Pareto front. This strategy represents a conceptual improvement over spaces computed by single-objective optimization. In addition, genetic programming (in particular gene expression programming) is used for finding analytic representations of the complex mappings generating the spaces (a composition of NDA and orthogonal principal components). The presented approach is domain independent and is illustrated via application to the geophysical prospecting of caves.

Stacking-sequence optimization for buckling of laminated plates by integer programming

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.; Walsh, Joanne L.

1991-01-01

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Deterministic Design Optimization of Structures in OpenMDAO Framework

NASA Technical Reports Server (NTRS)

Coroneos, Rula M.; Pai, Shantaram S.

2012-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

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

Graf, Peter; Dykes, Katherine; Scott, George

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

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.

Advanced induction accelerator designs for ground based and space based FELs

NASA Astrophysics Data System (ADS)

Birx, Daniel

1994-04-01

The primary goal of this program was to improve the performance of induction accelerators with particular regards to their being used to drive Free Electron Lasers (FEL's). It is hoped that FEL's operating at visible wavelengths might someday be used to beam power from earth to extraterrestrial locations. One application of this technology might be strategic theater defense, but this power source might be used to propel vehicles or supplement solar energized systems. Our path toward achieving this goal was directed first toward optimization of the nonlinear magnetic material used in induction accelerator construction and secondly at the overall design in terms of cost, size and efficiency. We began this research effort with an in depth study into the properties of various nonlinear magnetic materials. With the data on nonlinear magnetic materials, so important to the optimization of efficiency, in hand, we envisioned a new induction accelerator design where all of the components were packaged together in one container. This induction accelerator module would combine an /ll-solid-state, nonlinear magnetic driver and the induction accelerator cells all in one convenient package. Each accelerator module (denoted SNOMAD-IVB) would produce 1.0 MeV of acceleration with the exception of the SNOMAD-IV injector module which would produce 0.5 MeV of acceleration for an electron beam current up to 1000 amperes.

Enhanced nonlinearity interval mapping scheme for high-performance simulation-optimization of watershed-scale BMP placement

NASA Astrophysics Data System (ADS)

Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn

2015-03-01

Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity

NASA Astrophysics Data System (ADS)

Voronych, Oksana; Buraczewski, Adam; Matuszewski, Michał; Stobińska, Magdalena

2017-06-01

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton-polaritons. Catalogue identifier: AFBQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD-3 No. of lines in distributed program, including test data, etc.: 2157 No. of bytes in distributed program, including test data, etc.: 498994 Distribution format: tar.gz Programming language: C++ with OpenMP extensions (main numerical program), Python (helper scripts). Computer: Modern PC (tested on AMD and Intel processors), HP BL2x220. Operating system: Unix/Linux and Windows. Has the code been vectorized or parallelized?: Yes (OpenMP) RAM: 200 MB for single run Classification: 7, 7.7. Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Solution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware. Running time: 6h for 100 ps evolution, depending on the values of parameters

Superstructure-based Design and Optimization of Batch Biodiesel Production Using Heterogeneous Catalysts

NASA Astrophysics Data System (ADS)

Nuh, M. Z.; Nasir, N. F.

2017-08-01

Biodiesel as a fuel comprised of mono alkyl esters of long chain fatty acids derived from renewable lipid feedstock, such as vegetable oil and animal fat. Biodiesel production is complex process which need systematic design and optimization. However, no case study using the process system engineering (PSE) elements which are superstructure optimization of batch process, it involves complex problems and uses mixed-integer nonlinear programming (MINLP). The PSE offers a solution to complex engineering system by enabling the use of viable tools and techniques to better manage and comprehend the complexity of the system. This study is aimed to apply the PSE tools for the simulation of biodiesel process and optimization and to develop mathematical models for component of the plant for case A, B, C by using published kinetic data. Secondly, to determine economic analysis for biodiesel production, focusing on heterogeneous catalyst. Finally, the objective of this study is to develop the superstructure for biodiesel production by using heterogeneous catalyst. The mathematical models are developed by the superstructure and solving the resulting mixed integer non-linear model and estimation economic analysis by using MATLAB software. The results of the optimization process with the objective function of minimizing the annual production cost by batch process from case C is 23.2587 million USD. Overall, the implementation a study of process system engineering (PSE) has optimized the process of modelling, design and cost estimation. By optimizing the process, it results in solving the complex production and processing of biodiesel by batch.

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.

Optimization of cutting parameters for machining time in turning process

NASA Astrophysics Data System (ADS)

Mavliutov, A. R.; Zlotnikov, E. G.

2018-03-01

This paper describes the most effective methods for nonlinear constraint optimization of cutting parameters in the turning process. Among them are Linearization Programming Method with Dual-Simplex algorithm, Interior Point method, and Augmented Lagrangian Genetic Algorithm (ALGA). Every each of them is tested on an actual example – the minimization of production rate in turning process. The computation was conducted in the MATLAB environment. The comparative results obtained from the application of these methods show: The optimal value of the linearized objective and the original function are the same. ALGA gives sufficiently accurate values, however, when the algorithm uses the Hybrid function with Interior Point algorithm, the resulted values have the maximal accuracy.

A neural network strategy for end-point optimization of batch processes.

PubMed

Krothapally, M; Palanki, S

1999-01-01

The traditional way of operating batch processes has been to utilize an open-loop "golden recipe". However, there can be substantial batch to batch variation in process conditions and this open-loop strategy can lead to non-optimal operation. In this paper, a new approach is presented for end-point optimization of batch processes by utilizing neural networks. This strategy involves the training of two neural networks; one to predict switching times and the other to predict the input profile in the singular region. This approach alleviates the computational problems associated with the classical Pontryagin's approach and the nonlinear programming approach. The efficacy of this scheme is illustrated via simulation of a fed-batch fermentation.

PROFILE user's guide

NASA Technical Reports Server (NTRS)

Collins, L.; Saunders, D.

1986-01-01

User information for program PROFILE, an aerodynamics design utility for refining, plotting, and tabulating airfoil profiles is provided. The theory and implementation details for two of the more complex options are also presented. These are the REFINE option, for smoothing curvature in selected regions while retaining or seeking some specified thickness ratio, and the OPTIMIZE option, which seeks a specified curvature distribution. REFINE uses linear techniques to manipulate ordinates via the central difference approximation to second derivatives, while OPTIMIZE works directly with curvature using nonlinear least squares techniques. Use of programs QPLOT and BPLOT is also described, since all of the plots provided by PROFILE (airfoil coordinates, curvature distributions) are achieved via the general purpose QPLOT utility. BPLOT illustrates (again, via QPLOT) the shape functions used by two of PROFILE's options. The programs were designed and implemented for the Applied Aerodynamics Branch at NASA Ames Research Center, Moffett Field, California, and written in FORTRAN and run on a VAX-11/780 under VMS.

Shock and vibration technology with applications to electrical systems

NASA Technical Reports Server (NTRS)

Eshleman, R. L.

1972-01-01

A survey is presented of shock and vibration technology for electrical systems developed by the aerospace programs. The shock environment is surveyed along with new techniques for modeling, computer simulation, damping, and response analysis. Design techniques based on the use of analog computers, shock spectra, optimization, and nonlinear isolation are discussed. Shock mounting of rotors for performance and survival, and vibration isolation techniques are reviewed.

Robust optimization-based DC optimal power flow for managing wind generation uncertainty

NASA Astrophysics Data System (ADS)

Boonchuay, Chanwit; Tomsovic, Kevin; Li, Fangxing; Ongsakul, Weerakorn

2012-11-01

Integrating wind generation into the wider grid causes a number of challenges to traditional power system operation. Given the relatively large wind forecast errors, congestion management tools based on optimal power flow (OPF) need to be improved. In this paper, a robust optimization (RO)-based DCOPF is proposed to determine the optimal generation dispatch and locational marginal prices (LMPs) for a day-ahead competitive electricity market considering the risk of dispatch cost variation. The basic concept is to use the dispatch to hedge against the possibility of reduced or increased wind generation. The proposed RO-based DCOPF is compared with a stochastic non-linear programming (SNP) approach on a modified PJM 5-bus system. Primary test results show that the proposed DCOPF model can provide lower dispatch cost than the SNP approach.

Optimising the extraction rate of a non-durable non-renewable resource in a monopolistic market: a mathematical programming approach.

PubMed

Corominas, Albert; Fossas, Enric

2015-01-01

We assume a monopolistic market for a non-durable non-renewable resource such as crude oil, phosphates or fossil water. Stating the problem of obtaining optimal policies on extraction and pricing of the resource as a non-linear program allows general conclusions to be drawn under diverse assumptions about the demand curve, discount rates and length of the planning horizon. We compare the results with some common beliefs about the pace of exhaustion of this kind of resources.

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.

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.

Structural efficiency studies of corrugated compression panels with curved caps and beaded webs

NASA Technical Reports Server (NTRS)

Davis, R. C.; Mills, C. T.; Prabhakaran, R.; Jackson, L. R.

1984-01-01

Curved cross-sectional elements are employed in structural concepts for minimum-mass compression panels. Corrugated panel concepts with curved caps and beaded webs are optimized by using a nonlinear mathematical programming procedure and a rigorous buckling analysis. These panel geometries are shown to have superior structural efficiencies compared with known concepts published in the literature. Fabrication of these efficient corrugation concepts became possible by advances made in the art of superplastically forming of metals. Results of the mass optimization studies of the concepts are presented as structural efficiency charts for axial compression.

A Bell-Curved Based Algorithm for Mixed Continuous and Discrete Structural Optimization

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.; Weber, Michael; Sobieszczanski-Sobieski, Jaroslaw

2001-01-01

An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (mu + mu) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on 2-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).

Correlation techniques to determine model form in robust nonlinear system realization/identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1991-01-01

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

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.

Ant Colony Optimization for Markowitz Mean-Variance Portfolio Model

NASA Astrophysics Data System (ADS)

Deng, Guang-Feng; Lin, Woo-Tsong

This work presents Ant Colony Optimization (ACO), which was initially developed to be a meta-heuristic for combinatorial optimization, for solving the cardinality constraints Markowitz mean-variance portfolio model (nonlinear mixed quadratic programming problem). To our knowledge, an efficient algorithmic solution for this problem has not been proposed until now. Using heuristic algorithms in this case is imperative. Numerical solutions are obtained for five analyses of weekly price data for the following indices for the period March, 1992 to September, 1997: Hang Seng 31 in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei 225 in Japan. The test results indicate that the ACO is much more robust and effective than Particle swarm optimization (PSO), especially for low-risk investment portfolios.

Subjective audio quality evaluation of embedded-optimization-based distortion precompensation algorithms.

PubMed

Defraene, Bruno; van Waterschoot, Toon; Diehl, Moritz; Moonen, Marc

2016-07-01

Subjective audio quality evaluation experiments have been conducted to assess the performance of embedded-optimization-based precompensation algorithms for mitigating perceptible linear and nonlinear distortion in audio signals. It is concluded with statistical significance that the perceived audio quality is improved by applying an embedded-optimization-based precompensation algorithm, both in case (i) nonlinear distortion and (ii) a combination of linear and nonlinear distortion is present. Moreover, a significant positive correlation is reported between the collected subjective and objective PEAQ audio quality scores, supporting the validity of using PEAQ to predict the impact of linear and nonlinear distortion on the perceived audio quality.

Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions.

PubMed

Zaghian, Maryam; Cao, Wenhua; Liu, Wei; Kardar, Laleh; Randeniya, Sharmalee; Mohan, Radhe; Lim, Gino

2017-03-01

Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called "worst case dose" and "minmax" robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet tight dose limits. For robust optimization, the worst case dose approach was less sensitive to uncertainties than was the minmax approach for the prostate and skull-based cancer patients, whereas the minmax approach was superior for the head and neck cancer patients. The robustness of the IMPT plans was remarkably better after robust optimization than after PTV-based optimization, and the NLP-PTV-based optimization outperformed the LP-PTV-based optimization regarding robustness of clinical target volume coverage. In addition, plans generated using LP-based methods had notably fewer scanning spots than did those generated using NLP-based methods. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Mathematical programming formulations for satellite synthesis

NASA Technical Reports Server (NTRS)

Bhasin, Puneet; Reilly, Charles H.

1987-01-01

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Preliminary Design of Low-Thrust Interplanetary Missions

NASA Technical Reports Server (NTRS)

Sims, Jon A.; Flanagan, Steve N.

1997-01-01

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Improved Evolutionary Programming with Various Crossover Techniques for Optimal Power Flow Problem

NASA Astrophysics Data System (ADS)

Tangpatiphan, Kritsana; Yokoyama, Akihiko

This paper presents an Improved Evolutionary Programming (IEP) for solving the Optimal Power Flow (OPF) problem, which is considered as a non-linear, non-smooth, and multimodal optimization problem in power system operation. The total generator fuel cost is regarded as an objective function to be minimized. The proposed method is an Evolutionary Programming (EP)-based algorithm with making use of various crossover techniques, normally applied in Real Coded Genetic Algorithm (RCGA). The effectiveness of the proposed approach is investigated on the IEEE 30-bus system with three different types of fuel cost functions; namely the quadratic cost curve, the piecewise quadratic cost curve, and the quadratic cost curve superimposed by sine component. These three cost curves represent the generator fuel cost functions with a simplified model and more accurate models of a combined-cycle generating unit and a thermal unit with value-point loading effect respectively. The OPF solutions by the proposed method and Pure Evolutionary Programming (PEP) are observed and compared. The simulation results indicate that IEP requires less computing time than PEP with better solutions in some cases. Moreover, the influences of important IEP parameters on the OPF solution are described in details.

Development and Testing of Control Laws for the Active Aeroelastic Wing Program

NASA Technical Reports Server (NTRS)

Dibley, Ryan P.; Allen, Michael J.; Clarke, Robert; Gera, Joseph; Hodgkinson, John

2005-01-01

The Active Aeroelastic Wing research program was a joint program between the U.S. Air Force Research Laboratory and NASA established to investigate the characteristics of an aeroelastic wing and the technique of using wing twist for roll control. The flight test program employed the use of an F/A-18 aircraft modified by reducing the wing torsional stiffness and adding a custom research flight control system. The research flight control system was optimized to maximize roll rate using only wing surfaces to twist the wing while simultaneously maintaining design load limits, stability margins, and handling qualities. NASA Dryden Flight Research Center developed control laws using the software design tool called CONDUIT, which employs a multi-objective function optimization to tune selected control system design parameters. Modifications were made to the Active Aeroelastic Wing implementation in this new software design tool to incorporate the NASA Dryden Flight Research Center nonlinear F/A-18 simulation for time history analysis. This paper describes the design process, including how the control law requirements were incorporated into constraints for the optimization of this specific software design tool. Predicted performance is also compared to results from flight.

Optimal design of a gas transmission network: A case study of the Turkish natural gas pipeline network system

NASA Astrophysics Data System (ADS)

Gunes, Ersin Fatih

Turkey is located between Europe, which has increasing demand for natural gas and the geographies of Middle East, Asia and Russia, which have rich and strong natural gas supply. Because of the geographical location, Turkey has strategic importance according to energy sources. To supply this demand, a pipeline network configuration with the optimal and efficient lengths, pressures, diameters and number of compressor stations is extremely needed. Because, Turkey has a currently working and constructed network topology, obtaining an optimal configuration of the pipelines, including an optimal number of compressor stations with optimal locations, is the focus of this study. Identifying a network design with lowest costs is important because of the high maintenance and set-up costs. The quantity of compressor stations, the pipeline segments' lengths, the diameter sizes and pressures at compressor stations, are considered to be decision variables in this study. Two existing optimization models were selected and applied to the case study of Turkey. Because of the fixed cost of investment, both models are formulated as mixed integer nonlinear programs, which require branch and bound combined with the nonlinear programming solution methods. The differences between these two models are related to some factors that can affect the network system of natural gas such as wall thickness, material balance compressor isentropic head and amount of gas to be delivered. The results obtained by these two techniques are compared with each other and with the current system. Major differences between results are costs, pressures and flow rates. These solution techniques are able to find a solution with minimum cost for each model both of which are less than the current cost of the system while satisfying all the constraints on diameter, length, flow rate and pressure. These results give the big picture of an ideal configuration for the future state network for the country of Turkey.

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

NASA Technical Reports Server (NTRS)

Parrish, Nathan L.; Scheeres, Daniel J.

2017-01-01

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Using genetic algorithms to determine near-optimal pricing, investment and operating strategies in the electric power industry

NASA Astrophysics Data System (ADS)

Wu, Dongjun

Network industries have technologies characterized by a spatial hierarchy, the "network," with capital-intensive interconnections and time-dependent, capacity-limited flows of products and services through the network to customers. This dissertation studies service pricing, investment and business operating strategies for the electric power network. First-best solutions for a variety of pricing and investment problems have been studied. The evaluation of genetic algorithms (GA, which are methods based on the idea of natural evolution) as a primary means of solving complicated network problems, both w.r.t. pricing: as well as w.r.t. investment and other operating decisions, has been conducted. New constraint-handling techniques in GAs have been studied and tested. The actual application of such constraint-handling techniques in solving practical non-linear optimization problems has been tested on several complex network design problems with encouraging initial results. Genetic algorithms provide solutions that are feasible and close to optimal when the optimal solution is know; in some instances, the near-optimal solutions for small problems by the proposed GA approach can only be tested by pushing the limits of currently available non-linear optimization software. The performance is far better than several commercially available GA programs, which are generally inadequate in solving any of the problems studied in this dissertation, primarily because of their poor handling of constraints. Genetic algorithms, if carefully designed, seem very promising in solving difficult problems which are intractable by traditional analytic methods.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

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.

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.

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.; Rogers, James L., Jr.; Chang, Kwan J.

1987-01-01

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Lyapunov optimal feedback control of a nonlinear inverted pendulum

NASA Technical Reports Server (NTRS)

Grantham, W. J.; Anderson, M. J.

1989-01-01

Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Optimization under uncertainty of parallel nonlinear energy sinks

NASA Astrophysics Data System (ADS)

Boroson, Ethan; Missoum, Samy; Mattei, Pierre-Olivier; Vergez, Christophe

2017-04-01

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

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.

Transactions of The Army Conference on Applied Mathematics and Computing (5th) Held in West Point, New York on 15-18 June 1987

DTIC Science & Technology

1988-03-01

29 Statistical Machine Learning for the Cognitive Selection of Nonlinear Programming Algorithms in Engineering Design Optimization Toward...interpolation and Interpolation by Box Spline Surfaces Charles K. Chui, Harvey Diamond, Louise A. Raphael. 301 Knot Selection for Least Squares...West Virginia University, Morgantown, West Virginia; and Louise Raphael, National Science Foundation, Washington, DC Knot Selection for Least

Combinatorial approaches to gene recognition.

PubMed

Roytberg, M A; Astakhova, T V; Gelfand, M S

1997-01-01

Recognition of genes via exon assembly approaches leads naturally to the use of dynamic programming. We consider the general graph-theoretical formulation of the exon assembly problem and analyze in detail some specific variants: multicriterial optimization in the case of non-linear gene-scoring functions; context-dependent schemes for scoring exons and related procedures for exon filtering; and highly specific recognition of arbitrary gene segments, oligonucleotide probes and polymerase chain reaction (PCR) primers.

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.

Improvements to a method for the geometrically nonlinear analysis of compressively loaded stiffened composite panels

NASA Technical Reports Server (NTRS)

Stoll, Frederick

1993-01-01

The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.

Nonlinear histogram binning for quantitative analysis of lung tissue fibrosis in high-resolution CT data

NASA Astrophysics Data System (ADS)

Zavaletta, Vanessa A.; Bartholmai, Brian J.; Robb, Richard A.

2007-03-01

Diffuse lung diseases, such as idiopathic pulmonary fibrosis (IPF), can be characterized and quantified by analysis of volumetric high resolution CT scans of the lungs. These data sets typically have dimensions of 512 x 512 x 400. It is too subjective and labor intensive for a radiologist to analyze each slice and quantify regional abnormalities manually. Thus, computer aided techniques are necessary, particularly texture analysis techniques which classify various lung tissue types. Second and higher order statistics which relate the spatial variation of the intensity values are good discriminatory features for various textures. The intensity values in lung CT scans range between [-1024, 1024]. Calculation of second order statistics on this range is too computationally intensive so the data is typically binned between 16 or 32 gray levels. There are more effective ways of binning the gray level range to improve classification. An optimal and very efficient way to nonlinearly bin the histogram is to use a dynamic programming algorithm. The objective of this paper is to show that nonlinear binning using dynamic programming is computationally efficient and improves the discriminatory power of the second and higher order statistics for more accurate quantification of diffuse lung disease.

Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings.

PubMed

Qiu, Cheng-Wei; Hu, Li; Zhang, Baile; Wu, Bae-Ian; Johnson, Steven G; Joannopoulos, John D

2009-08-03

Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical simulation of not only near-field electric-field distribution but also the far-field radar cross section (RCS).

An intelligent emissions controller for fuel lean gas reburn in coal-fired power plants.

PubMed

Reifman, J; Feldman, E E; Wei, T Y; Glickert, R W

2000-02-01

The application of artificial intelligence techniques for performance optimization of the fuel lean gas reburn (FLGR) system is investigated. A multilayer, feedforward artificial neural network is applied to model static nonlinear relationships between the distribution of injected natural gas into the upper region of the furnace of a coal-fired boiler and the corresponding oxides of nitrogen (NOx) emissions exiting the furnace. Based on this model, optimal distributions of injected gas are determined such that the largest NOx reduction is achieved for each value of total injected gas. This optimization is accomplished through the development of a new optimization method based on neural networks. This new optimal control algorithm, which can be used as an alternative generic tool for solving multidimensional nonlinear constrained optimization problems, is described and its results are successfully validated against an off-the-shelf tool for solving mathematical programming problems. Encouraging results obtained using plant data from one of Commonwealth Edison's coal-fired electric power plants demonstrate the feasibility of the overall approach. Preliminary results show that the use of this intelligent controller will also enable the determination of the most cost-effective operating conditions of the FLGR system by considering, along with the optimal distribution of the injected gas, the cost differential between natural gas and coal and the open-market price of NOx emission credits. Further study, however, is necessary, including the construction of a more comprehensive database, needed to develop high-fidelity process models and to add carbon monoxide (CO) emissions to the model of the gas reburn system.

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

DOE PAGES

Li, Mingjie; Zhou, Ping; Wang, Hong; ...

2017-09-19

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refiningmore » system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.« less

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

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

Li, Mingjie; Zhou, Ping; Wang, Hong

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refiningmore » system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.« less

Hybrid Genetic Agorithms and Line Search Method for Industrial Production Planning with Non-Linear Fitness Function

NASA Astrophysics Data System (ADS)

Vasant, Pandian; Barsoum, Nader

2008-10-01

Many engineering, science, information technology and management optimization problems can be considered as non linear programming real world problems where the all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers which was represented by logistic membership functions by using hybrid evolutionary optimization approach. To explore the applicability of the present study a numerical example is considered to determine the production planning for the decision variables and profit of the company.

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles R.

2018-02-01

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

Optimization Design of Minimum Total Resistance Hull Form Based on CFD Method

NASA Astrophysics Data System (ADS)

Zhang, Bao-ji; Zhang, Sheng-long; Zhang, Hui

2018-06-01

In order to reduce the resistance and improve the hydrodynamic performance of a ship, two hull form design methods are proposed based on the potential flow theory and viscous flow theory. The flow fields are meshed using body-fitted mesh and structured grids. The parameters of the hull modification function are the design variables. A three-dimensional modeling method is used to alter the geometry. The Non-Linear Programming (NLP) method is utilized to optimize a David Taylor Model Basin (DTMB) model 5415 ship under the constraints, including the displacement constraint. The optimization results show an effective reduction of the resistance. The two hull form design methods developed in this study can provide technical support and theoretical basis for designing green ships.

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.

A superlinear interior points algorithm for engineering design optimization

NASA Technical Reports Server (NTRS)

Herskovits, J.; Asquier, J.

1990-01-01

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

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.

MIDACO on MINLP space applications

NASA Astrophysics Data System (ADS)

Schlueter, Martin; Erb, Sven O.; Gerdts, Matthias; Kemble, Stephen; Rückmann, Jan-J.

2013-04-01

A numerical study on two challenging mixed-integer non-linear programming (MINLP) space applications and their optimization with MIDACO, a recently developed general purpose optimization software, is presented. These applications are the optimal control of the ascent of a multiple-stage space launch vehicle and the space mission trajectory design from Earth to Jupiter using multiple gravity assists. Additionally, an NLP aerospace application, the optimal control of an F8 aircraft manoeuvre, is discussed and solved. In order to enhance the optimization performance of MIDACO a hybridization technique, coupling MIDACO with an SQP algorithm, is presented for two of these three applications. The numerical results show, that the applications can be solved to their best known solution (or even new best solution) in a reasonable time by the considered approach. Since using the concept of MINLP is still a novelty in the field of (aero)space engineering, the demonstrated capabilities are seen as very promising.

Reduction of the Nonlinear Phase Shift Induced by Stimulated Brillouin Scattering for Bi-Directional Pumping Configuration System Using Particle Swarm Optimization Algorithm

NASA Astrophysics Data System (ADS)

Al-Asadi, H. A.

2013-02-01

We present a theoretical analysis of an additional nonlinear phase shift of backward Stokes wave based on stimulated Brillouin scattering in the system with a bi-directional pumping scheme. We optimize three parameters of the system: the numerical aperture, the optical loss and the pumping wavelength to minimize an additional nonlinear phase shift of backward Stokes waves due to stimulated Brillouin scattering. The optimization is performed with various Brillouin pump powers and the optical reflectivity values are based on the modern, global evolutionary computation algorithm, particle swarm optimization. It is shown that the additional nonlinear phase shift of backward Stokes wave varies with different optical fiber lengths, and can be minimized to less than 0.07 rad according to the particle swarm optimization algorithm for 5 km. The bi-directional pumping configuration system is shown to be efficient when it is possible to transmit the power output to advanced when frequency detuning is negative and delayed when it is positive, with the optimum values of the three parameters to achieve the reduction of an additional nonlinear phase shift.

Optimization of autoregressive, exogenous inputs-based typhoon inundation forecasting models using a multi-objective genetic algorithm

NASA Astrophysics Data System (ADS)

Ouyang, Huei-Tau

2017-07-01

Three types of model for forecasting inundation levels during typhoons were optimized: the linear autoregressive model with exogenous inputs (LARX), the nonlinear autoregressive model with exogenous inputs with wavelet function (NLARX-W) and the nonlinear autoregressive model with exogenous inputs with sigmoid function (NLARX-S). The forecast performance was evaluated by three indices: coefficient of efficiency, error in peak water level and relative time shift. Historical typhoon data were used to establish water-level forecasting models that satisfy all three objectives. A multi-objective genetic algorithm was employed to search for the Pareto-optimal model set that satisfies all three objectives and select the ideal models for the three indices. Findings showed that the optimized nonlinear models (NLARX-W and NLARX-S) outperformed the linear model (LARX). Among the nonlinear models, the optimized NLARX-W model achieved a more balanced performance on the three indices than the NLARX-S models and is recommended for inundation forecasting during typhoons.

Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

PubMed

Yang, Xiong; He, Haibo

2018-05-26

In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.

DYCAST: A finite element program for the crash analysis of structures

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.; Ogilvie, P.

1987-01-01

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

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

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

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

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

NASA Technical Reports Server (NTRS)

Hargrove, A.

1982-01-01

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

NASA Astrophysics Data System (ADS)

Ma, Lin; Wang, Kexin; Xu, Zuhua; Shao, Zhijiang; Song, Zhengyu; Biegler, Lorenz T.

2018-05-01

This study presents a trajectory optimization framework for lunar rover performing vertical takeoff vertical landing (VTVL) maneuvers in the presence of terrain using variable-thrust propulsion. First, a VTVL trajectory optimization problem with three-dimensional kinematics and dynamics model, boundary conditions, and path constraints is formulated. Then, a finite-element approach transcribes the formulated trajectory optimization problem into a nonlinear programming (NLP) problem solved by a highly efficient NLP solver. A homotopy-based backtracking strategy is applied to enhance the convergence in solving the formulated VTVL trajectory optimization problem. The optimal thrust solution typically has a "bang-bang" profile considering that bounds are imposed on the magnitude of engine thrust. An adaptive mesh refinement strategy based on a constant Hamiltonian profile is designed to address the difficulty in locating the breakpoints in the thrust profile. Four scenarios are simulated. Simulation results indicate that the proposed trajectory optimization framework has sufficient adaptability to handle VTVL missions efficiently.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Model and Algorithm for Substantiating Solutions for Organization of High-Rise Construction Project

NASA Astrophysics Data System (ADS)

Anisimov, Vladimir; Anisimov, Evgeniy; Chernysh, Anatoliy

2018-03-01

In the paper the models and the algorithm for the optimal plan formation for the organization of the material and logistical processes of the high-rise construction project and their financial support are developed. The model is based on the representation of the optimization procedure in the form of a non-linear problem of discrete programming, which consists in minimizing the execution time of a set of interrelated works by a limited number of partially interchangeable performers while limiting the total cost of performing the work. The proposed model and algorithm are the basis for creating specific organization management methodologies for the high-rise construction project.

Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle.

PubMed

Prado, Igor Afonso Acampora; Pereira, Mateus de Freitas Virgílio; de Castro, Davi Ferreira; Dos Santos, Davi Antônio; Balthazar, Jose Manoel

2018-06-01

The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Development of a turbomachinery design optimization procedure using a multiple-parameter nonlinear perturbation method

NASA Technical Reports Server (NTRS)

Stahara, S. S.

1984-01-01

An investigation was carried out to complete the preliminary development of a combined perturbation/optimization procedure and associated computational code for designing optimized blade-to-blade profiles of turbomachinery blades. The overall purpose of the procedures developed is to provide demonstration of a rapid nonlinear perturbation method for minimizing the computational requirements associated with parametric design studies of turbomachinery flows. The method combines the multiple parameter nonlinear perturbation method, successfully developed in previous phases of this study, with the NASA TSONIC blade-to-blade turbomachinery flow solver, and the COPES-CONMIN optimization procedure into a user's code for designing optimized blade-to-blade surface profiles of turbomachinery blades. Results of several design applications and a documented version of the code together with a user's manual are provided.

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

PubMed Central

Morris, Melody K.; Saez-Rodriguez, Julio; Lauffenburger, Douglas A.; Alexopoulos, Leonidas G.

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms. PMID:23226239

Optimization of Residual Stresses in MMC's through Process Parameter Control and the use of Heterogeneous Compensating/Compliant Interfacial Layers. OPTCOMP2 User's Guide

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Salzar, Robert S.

1996-01-01

A user's guide for the computer program OPTCOMP2 is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in unidirectional metal matrix composites subjected to combined thermomechanical axisymmetric loading by altering the processing history, as well as through the microstructural design of interfacial fiber coatings. The user specifies the initial architecture of the composite and the load history, with the constituent materials being elastic, plastic, viscoplastic, or as defined by the 'user-defined' constitutive model, in addition to the objective function and constraints, through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the inelastic response of a fiber/interface layer(s)/matrix concentric cylinder model where the interface layers can be either homogeneous or heterogeneous. The response of heterogeneous layers is modeled using Aboudi's three-dimensional method of cells micromechanics model. The commercial optimization package DOT is used for the nonlinear optimization problem. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.

Non Linear Programming (NLP) formulation for quantitative modeling of protein signal transduction pathways.

PubMed

Mitsos, Alexander; Melas, Ioannis N; Morris, Melody K; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Alexopoulos, Leonidas G

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.

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.

Annual Review of Research under the Joint Services Electronics Program,

DTIC Science & Technology

1981-12-01

nonlinear system under investigation to be transformed, without approximation, into an equivalent linear system to which classical design methodologies are...employed his work in the design of an experimental helicopter autopilot which is presently under- going simulation and is expected to fly in the near...decentralized, and non -quad- duced from that which would be required ratic systems is presented. Here, one for an optimal non -linlar controller. designs a

A multiobjective optimization model and an orthogonal design-based hybrid heuristic algorithm for regional urban mining management problems.

PubMed

Wu, Hao; Wan, Zhong

2018-02-01

In this paper, a multiobjective mixed-integer piecewise nonlinear programming model (MOMIPNLP) is built to formulate the management problem of urban mining system, where the decision variables are associated with buy-back pricing, choices of sites, transportation planning, and adjustment of production capacity. Different from the existing approaches, the social negative effect, generated from structural optimization of the recycling system, is minimized in our model, as well as the total recycling profit and utility from environmental improvement are jointly maximized. For solving the problem, the MOMIPNLP model is first transformed into an ordinary mixed-integer nonlinear programming model by variable substitution such that the piecewise feature of the model is removed. Then, based on technique of orthogonal design, a hybrid heuristic algorithm is developed to find an approximate Pareto-optimal solution, where genetic algorithm is used to optimize the structure of search neighborhood, and both local branching algorithm and relaxation-induced neighborhood search algorithm are employed to cut the searching branches and reduce the number of variables in each branch. Numerical experiments indicate that this algorithm spends less CPU (central processing unit) time in solving large-scale regional urban mining management problems, especially in comparison with the similar ones available in literature. By case study and sensitivity analysis, a number of practical managerial implications are revealed from the model. Since the metal stocks in society are reliable overground mineral sources, urban mining has been paid great attention as emerging strategic resources in an era of resource shortage. By mathematical modeling and development of efficient algorithms, this paper provides decision makers with useful suggestions on the optimal design of recycling system in urban mining. For example, this paper can answer how to encourage enterprises to join the recycling activities by government's support and subsidies, whether the existing recycling system can meet the developmental requirements or not, and what is a reasonable adjustment of production capacity.

UCAV path planning in the presence of radar-guided surface-to-air missile threats

NASA Astrophysics Data System (ADS)

Zeitz, Frederick H., III

This dissertation addresses the problem of path planning for unmanned combat aerial vehicles (UCAVs) in the presence of radar-guided surface-to-air missiles (SAMs). The radars, collocated with SAM launch sites, operate within the structure of an Integrated Air Defense System (IADS) that permits communication and cooperation between individual radars. The problem is formulated in the framework of the interaction between three sub-systems: the aircraft, the IADS, and the missile. The main features of this integrated model are: The aircraft radar cross section (RCS) depends explicitly on both the aspect and bank angles; hence, the RCS and aircraft dynamics are coupled. The probabilistic nature of IADS tracking is accounted for; namely, the probability that the aircraft has been continuously tracked by the IADS depends on the aircraft RCS and range from the perspective of each radar within the IADS. Finally, the requirement to maintain tracking prior to missile launch and during missile flyout are also modeled. Based on this model, the problem of UCAV path planning is formulated as a minimax optimal control problem, with the aircraft bank angle serving as control. Necessary conditions of optimality for this minimax problem are derived. Based on these necessary conditions, properties of the optimal paths are derived. These properties are used to discretize the dynamic optimization problem into a finite-dimensional, nonlinear programming problem that can be solved numerically. Properties of the optimal paths are also used to initialize the numerical procedure. A homotopy method is proposed to solve the finite-dimensional, nonlinear programming problem, and a heuristic method is proposed to improve the discretization during the homotopy process. Based upon the properties of numerical solutions, a method is proposed for parameterizing and storing information for later recall in flight to permit rapid replanning in response to changing threats. Illustrative examples are presented that confirm the standard flying tactics of "denying range, aspect, and aim," by yielding flight paths that "weave" to avoid long exposures of aspects with large RCS.

Design of a nonlinear torsional vibration absorber

NASA Astrophysics Data System (ADS)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.

Ascent trajectory optimization for stratospheric airship with thermal effects

NASA Astrophysics Data System (ADS)

Guo, Xiao; Zhu, Ming

2013-09-01

Ascent trajectory optimization with thermal effects is addressed for a stratospheric airship. Basic thermal characteristics of the stratospheric airship are introduced. Besides, the airship’s equations of motion are constructed by including the factors about aerodynamic force, added mass and wind profiles which are developed based on horizontal-wind model. For both minimum-time and minimum-energy flights during ascent, the trajectory optimization problem is described with the path and terminal constraints in different scenarios and then, is converted into a parameter optimization problem by a direct collocation method. Sparse Nonlinear OPTimizer(SNOPT) is employed as a nonlinear programming solver and two scenarios are adopted. The solutions obtained illustrate that the trajectories are greatly affected by the thermal behaviors which prolong the daytime minimum-time flights of about 20.8% compared with that of nighttime in scenario 1 and of about 10.5% in scenario 2. And there is the same trend for minimum-energy flights. For the energy consumption of minimum-time flights, 6% decrease is abstained in scenario 1 and 5% decrease in scenario 2. However, a few energy consumption reduction is achieved for minimum-energy flights. Solar radiation is the principal component and the natural wind also affects the thermal behaviors of stratospheric airship during ascent. The relationship between take-off time and performance of airship during ascent is discussed. it is found that the take-off time at dusk is best choice for stratospheric airship. And in addition, for saving energy, airship prefers to fly downwind.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2

NASA Technical Reports Server (NTRS)

1972-01-01

The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China.

PubMed

Zhang, Liping; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2014-06-01

In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO-NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt-Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt-Winters exponential smoothing method. Copyright © 2014. Published by Elsevier Ltd.

Solution of the Generalized Noah's Ark Problem.

PubMed

Billionnet, Alain

2013-01-01

The phylogenetic diversity (PD) of a set of species is a measure of the evolutionary distance among the species in the collection, based on a phylogenetic tree. Such a tree is composed of a root, internal nodes, and leaves that correspond to the set of taxa under study. With each edge of the tree is associated a non-negative branch length (evolutionary distance). If a particular survival probability is associated with each taxon, the PD measure becomes the expected PD measure. In the Noah's Ark Problem (NAP) introduced by Weitzman (1998), these survival probabilities can be increased at some cost. The problem is to determine how best to allocate a limited amount of resources to maximize the expected PD of the considered species. It is easy to formulate the NAP as a (difficult) nonlinear 0-1 programming problem. The aim of this article is to show that a general version of the NAP (GNAP) can be solved simply and efficiently with any set of edge weights and any set of survival probabilities by using standard mixed-integer linear programming software. The crucial point to move from a nonlinear program in binary variables to a mixed-integer linear program, is to approximate the logarithmic function by the lower envelope of a set of tangents to the curve. Solving the obtained mixed-integer linear program provides not only a near-optimal solution but also an upper bound on the value of the optimal solution. We also applied this approach to a generalization of the nature reserve problem (GNRP) that consists of selecting a set of regions to be conserved so that the expected PD of the set of species present in these regions is maximized. In this case, the survival probabilities of different taxa are not independent of each other. Computational results are presented to illustrate potentialities of the approach. Near-optimal solutions with hypothetical phylogenetic trees comprising about 4000 taxa are obtained in a few seconds or minutes of computing time for the GNAP, and in about 30 min for the GNRP. In all the cases the average guarantee varies from 0% to 1.20%.

Optimal Averages for Nonlinear Signal Decompositions - Another Alternative for Empirical Mode Decomposition

DTIC Science & Technology

2014-10-01

nonlinear and non-stationary signals. It aims at decomposing a signal, via an iterative sifting procedure, into several intrinsic mode functions ...stationary signals. It aims at decomposing a signal, via an iterative sifting procedure into several intrinsic mode functions (IMFs), and each of the... function , optimization. 1 Introduction It is well known that nonlinear and non-stationary signal analysis is important and difficult. His- torically

Support vector machine firefly algorithm based optimization of lens system.

PubMed

Shamshirband, Shahaboddin; Petković, Dalibor; Pavlović, Nenad T; Ch, Sudheer; Altameem, Torki A; Gani, Abdullah

2015-01-01

Lens system design is an important factor in image quality. The main aspect of the lens system design methodology is the optimization procedure. Since optimization is a complex, nonlinear task, soft computing optimization algorithms can be used. There are many tools that can be employed to measure optical performance, but the spot diagram is the most useful. The spot diagram gives an indication of the image of a point object. In this paper, the spot size radius is considered an optimization criterion. Intelligent soft computing scheme support vector machines (SVMs) coupled with the firefly algorithm (FFA) are implemented. The performance of the proposed estimators is confirmed with the simulation results. The result of the proposed SVM-FFA model has been compared with support vector regression (SVR), artificial neural networks, and generic programming methods. The results show that the SVM-FFA model performs more accurately than the other methodologies. Therefore, SVM-FFA can be used as an efficient soft computing technique in the optimization of lens system designs.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

Optimization methods for decision making in disease prevention and epidemic control.

PubMed

Deng, Yan; Shen, Siqian; Vorobeychik, Yevgeniy

2013-11-01

This paper investigates problems of disease prevention and epidemic control (DPEC), in which we optimize two sets of decisions: (i) vaccinating individuals and (ii) closing locations, given respective budgets with the goal of minimizing the expected number of infected individuals after intervention. The spread of diseases is inherently stochastic due to the uncertainty about disease transmission and human interaction. We use a bipartite graph to represent individuals' propensities of visiting a set of location, and formulate two integer nonlinear programming models to optimize choices of individuals to vaccinate and locations to close. Our first model assumes that if a location is closed, its visitors stay in a safe location and will not visit other locations. Our second model incorporates compensatory behavior by assuming multiple behavioral groups, always visiting the most preferred locations that remain open. The paper develops algorithms based on a greedy strategy, dynamic programming, and integer programming, and compares the computational efficacy and solution quality. We test problem instances derived from daily behavior patterns of 100 randomly chosen individuals (corresponding to 195 locations) in Portland, Oregon, and provide policy insights regarding the use of the two DPEC models. Copyright © 2013 Elsevier Inc. All rights reserved.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

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

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

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.

Human motion planning based on recursive dynamics and optimal control techniques

NASA Technical Reports Server (NTRS)

Lo, Janzen; Huang, Gang; Metaxas, Dimitris

2002-01-01

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Active Nonlinear Feedback Control for Aerospace Systems. Processor

DTIC Science & Technology

1990-12-01

relating to the role of nonlinearities in feedback control. These area include Lyapunov function theory, chaotic controllers, statistical energy analysis , phase robustness, and optimal nonlinear control theory.

Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers

NASA Astrophysics Data System (ADS)

Talatahari, Siamak; Rahbari, Nima Mohajer

2015-10-01

In the current research, the imperialist competitive algorithm is dramatically enhanced and a new optimization method dubbed as Enriched Imperialist Competitive Algorithm (EICA) is effectively introduced to deal with high non-linear optimization problems. To conduct a close examination of its functionality and efficacy, the proposed metaheuristic optimization approach is actively employed to sort out the parameter identification of two different types of hysteretic Bouc-Wen models which are simulating the non-linear behavior of MR dampers. Two types of experimental data are used for the optimization problems to minutely examine the robustness of the proposed EICA. The obtained results self-evidently demonstrate the high adaptability of EICA to suitably get to the bottom of such non-linear and hysteretic problems.

The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients

NASA Astrophysics Data System (ADS)

Dmitriev, Mikhail G.; Makarov, Dmitry A.

2016-08-01

We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.

Optimization of groundwater artificial recharge systems using a genetic algorithm: a case study in Beijing, China

NASA Astrophysics Data System (ADS)

Hao, Qichen; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Huang, Linxian

2018-05-01

An optimization approach is used for the operation of groundwater artificial recharge systems in an alluvial fan in Beijing, China. The optimization model incorporates a transient groundwater flow model, which allows for simulation of the groundwater response to artificial recharge. The facilities' operation with regard to recharge rates is formulated as a nonlinear programming problem to maximize the volume of surface water recharged into the aquifers under specific constraints. This optimization problem is solved by the parallel genetic algorithm (PGA) based on OpenMP, which could substantially reduce the computation time. To solve the PGA with constraints, the multiplicative penalty method is applied. In addition, the facilities' locations are implicitly determined on the basis of the results of the recharge-rate optimizations. Two scenarios are optimized and the optimal results indicate that the amount of water recharged into the aquifers will increase without exceeding the upper limits of the groundwater levels. Optimal operation of this artificial recharge system can also contribute to the more effective recovery of the groundwater storage capacity.

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.

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

A Simulation-Optimization Model for the Management of Seawater Intrusion

NASA Astrophysics Data System (ADS)

Stanko, Z.; Nishikawa, T.

2012-12-01

Seawater intrusion is a common problem in coastal aquifers where excessive groundwater pumping can lead to chloride contamination of a freshwater resource. Simulation-optimization techniques have been developed to determine optimal management strategies while mitigating seawater intrusion. The simulation models are often density-independent groundwater-flow models that may assume a sharp interface and/or use equivalent freshwater heads. The optimization methods are often linear-programming (LP) based techniques that that require simplifications of the real-world system. However, seawater intrusion is a highly nonlinear, density-dependent flow and transport problem, which requires the use of nonlinear-programming (NLP) or global-optimization (GO) techniques. NLP approaches are difficult because of the need for gradient information; therefore, we have chosen a GO technique for this study. Specifically, we have coupled a multi-objective genetic algorithm (GA) with a density-dependent groundwater-flow and transport model to simulate and identify strategies that optimally manage seawater intrusion. GA is a heuristic approach, often chosen when seeking optimal solutions to highly complex and nonlinear problems where LP or NLP methods cannot be applied. The GA utilized in this study is the Epsilon-Nondominated Sorted Genetic Algorithm II (ɛ-NSGAII), which can approximate a pareto-optimal front between competing objectives. This algorithm has several key features: real and/or binary variable capabilities; an efficient sorting scheme; preservation and diversity of good solutions; dynamic population sizing; constraint handling; parallelizable implementation; and user controlled precision for each objective. The simulation model is SEAWAT, the USGS model that couples MODFLOW with MT3DMS for variable-density flow and transport. ɛ-NSGAII and SEAWAT were efficiently linked together through a C-Fortran interface. The simulation-optimization model was first tested by using a published density-independent flow model test case that was originally solved using a sequential LP method with the USGS's Ground-Water Management Process (GWM). For the problem formulation, the objective is to maximize net groundwater extraction, subject to head and head-gradient constraints. The decision variables are pumping rates at fixed wells and the system's state is represented with freshwater hydraulic head. The results of the proposed algorithm were similar to the published results (within 1%); discrepancies may be attributed to differences in the simulators and inherent differences between LP and GA. The GWM test case was then extended to a density-dependent flow and transport version. As formulated, the optimization problem is infeasible because of the density effects on hydraulic head. Therefore, the sum of the squared constraint violation (SSC) was used as a second objective. The result is a pareto curve showing optimal pumping rates versus the SSC. Analysis of this curve indicates that a similar net-extraction rate to the test case can be obtained with a minor violation in vertical head-gradient constraints. This study shows that a coupled ɛ-NSGAII/SEAWAT model can be used for the management of groundwater seawater intrusion. In the future, the proposed methodology will be applied to a real-world seawater intrusion and resource management problem for Santa Barbara, CA.

A flexible, interactive software tool for fitting the parameters of neuronal models.

PubMed

Friedrich, Péter; Vella, Michael; Gulyás, Attila I; Freund, Tamás F; Káli, Szabolcs

2014-01-01

The construction of biologically relevant neuronal models as well as model-based analysis of experimental data often requires the simultaneous fitting of multiple model parameters, so that the behavior of the model in a certain paradigm matches (as closely as possible) the corresponding output of a real neuron according to some predefined criterion. Although the task of model optimization is often computationally hard, and the quality of the results depends heavily on technical issues such as the appropriate choice (and implementation) of cost functions and optimization algorithms, no existing program provides access to the best available methods while also guiding the user through the process effectively. Our software, called Optimizer, implements a modular and extensible framework for the optimization of neuronal models, and also features a graphical interface which makes it easy for even non-expert users to handle many commonly occurring scenarios. Meanwhile, educated users can extend the capabilities of the program and customize it according to their needs with relatively little effort. Optimizer has been developed in Python, takes advantage of open-source Python modules for nonlinear optimization, and interfaces directly with the NEURON simulator to run the models. Other simulators are supported through an external interface. We have tested the program on several different types of problems of varying complexity, using different model classes. As targets, we used simulated traces from the same or a more complex model class, as well as experimental data. We successfully used Optimizer to determine passive parameters and conductance densities in compartmental models, and to fit simple (adaptive exponential integrate-and-fire) neuronal models to complex biological data. Our detailed comparisons show that Optimizer can handle a wider range of problems, and delivers equally good or better performance than any other existing neuronal model fitting tool.

A flexible, interactive software tool for fitting the parameters of neuronal models

PubMed Central

Friedrich, Péter; Vella, Michael; Gulyás, Attila I.; Freund, Tamás F.; Káli, Szabolcs

2014-01-01

The construction of biologically relevant neuronal models as well as model-based analysis of experimental data often requires the simultaneous fitting of multiple model parameters, so that the behavior of the model in a certain paradigm matches (as closely as possible) the corresponding output of a real neuron according to some predefined criterion. Although the task of model optimization is often computationally hard, and the quality of the results depends heavily on technical issues such as the appropriate choice (and implementation) of cost functions and optimization algorithms, no existing program provides access to the best available methods while also guiding the user through the process effectively. Our software, called Optimizer, implements a modular and extensible framework for the optimization of neuronal models, and also features a graphical interface which makes it easy for even non-expert users to handle many commonly occurring scenarios. Meanwhile, educated users can extend the capabilities of the program and customize it according to their needs with relatively little effort. Optimizer has been developed in Python, takes advantage of open-source Python modules for nonlinear optimization, and interfaces directly with the NEURON simulator to run the models. Other simulators are supported through an external interface. We have tested the program on several different types of problems of varying complexity, using different model classes. As targets, we used simulated traces from the same or a more complex model class, as well as experimental data. We successfully used Optimizer to determine passive parameters and conductance densities in compartmental models, and to fit simple (adaptive exponential integrate-and-fire) neuronal models to complex biological data. Our detailed comparisons show that Optimizer can handle a wider range of problems, and delivers equally good or better performance than any other existing neuronal model fitting tool. PMID:25071540

Application of multi-objective nonlinear optimization technique for coordinated ramp-metering

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

Haj Salem, Habib; Farhi, Nadir; Lebacque, Jean Patrick, E-mail: abib.haj-salem@ifsttar.fr, E-mail: nadir.frahi@ifsttar.fr, E-mail: jean-patrick.lebacque@ifsttar.fr

2015-03-10

This paper aims at developing a multi-objective nonlinear optimization algorithm applied to coordinated motorway ramp metering. The multi-objective function includes two components: traffic and safety. Off-line simulation studies were performed on A4 France Motorway including 4 on-ramps.

Estimating linear-nonlinear models using Rényi divergences

PubMed Central

Kouh, Minjoon; Sharpee, Tatyana O.

2009-01-01

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data. PMID:19568981

Estimating linear-nonlinear models using Renyi divergences.

PubMed

Kouh, Minjoon; Sharpee, Tatyana O

2009-01-01

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Optimal nonlinear codes for the perception of natural colours.

PubMed

von der Twer, T; MacLeod, D I

2001-08-01

We discuss how visual nonlinearity can be optimized for the precise representation of environmental inputs. Such optimization leads to neural signals with a compressively nonlinear input-output function the gradient of which is matched to the cube root of the probability density function (PDF) of the environmental input values (and not to the PDF directly as in histogram equalization). Comparisons between theory and psychophysical and electrophysiological data are roughly consistent with the idea that parvocellular (P) cells are optimized for precision representation of colour: their contrast-response functions span a range appropriately matched to the environmental distribution of natural colours along each dimension of colour space. Thus P cell codes for colour may have been selected to minimize error in the perceptual estimation of stimulus parameters for natural colours. But magnocellular (M) cells have a much stronger than expected saturating nonlinearity; this supports the view that the function of M cells is mainly to detect boundaries rather than to specify contrast or lightness.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Application of decomposition techniques to the preliminary design of a transport aircraft

NASA Technical Reports Server (NTRS)

Rogan, J. E.; Mcelveen, R. P.; Kolb, M. A.

1986-01-01

A multifaceted decomposition of a nonlinear constrained optimization problem describing the preliminary design process for a transport aircraft has been made. Flight dynamics, flexible aircraft loads and deformations, and preliminary structural design subproblems appear prominently in the decomposition. The use of design process decomposition for scheduling design projects, a new system integration approach to configuration control, and the application of object-centered programming to a new generation of design tools are discussed.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

A robust and high precision optimal explicit guidance scheme for solid motor propelled launch vehicles with thrust and drag uncertainty

NASA Astrophysics Data System (ADS)

Maity, Arnab; Padhi, Radhakant; Mallaram, Sanjeev; Mallikarjuna Rao, G.; Manickavasagam, M.

2016-10-01

A new nonlinear optimal and explicit guidance law is presented in this paper for launch vehicles propelled by solid motors. It can ensure very high terminal precision despite not having the exact knowledge of the thrust-time curve apriori. This was motivated from using it for a carrier launch vehicle in a hypersonic mission, which demands an extremely narrow terminal accuracy window for the launch vehicle for successful initiation of operation of the hypersonic vehicle. The proposed explicit guidance scheme, which computes the optimal guidance command online, ensures the required stringent final conditions with high precision at the injection point. A key feature of the proposed guidance law is an innovative extension of the recently developed model predictive static programming guidance with flexible final time. A penalty function approach is also followed to meet the input and output inequality constraints throughout the vehicle trajectory. In this paper, the guidance law has been successfully validated from nonlinear six degree-of-freedom simulation studies by designing an inner-loop autopilot as well, which enhances confidence of its usefulness significantly. In addition to excellent nominal results, the proposed guidance has been found to have good robustness for perturbed cases as well.

Development and Application of a Tool for Optimizing Composite Matrix Viscoplastic Material Parameters

NASA Technical Reports Server (NTRS)

Murthy, Pappu L. N.; Naghipour Ghezeljeh, Paria; Bednarcyk, Brett A.

2018-01-01

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) and its application. MAC/GMC is a composite material and laminate analysis software package developed at NASA Glenn Research Center. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that helps users optimize highly nonlinear viscoplastic constitutive law parameters by fitting experimentally observed/measured stress-strain responses under various thermo-mechanical conditions for braided composites. The tool has been developed utilizing the MATrix LABoratory (MATLAB) (The Mathworks, Inc., Natick, MA) programming language. Illustrative examples shown are for a specific braided composite system wherein the matrix viscoplastic behavior is represented by a constitutive law described by seven parameters. The tool is general enough to fit any number of experimentally observed stress-strain responses of the material. The number of parameters to be optimized, as well as the importance given to each stress-strain response, are user choice. Three different optimization algorithms are included: (1) Optimization based on gradient method, (2) Genetic algorithm (GA) based optimization and (3) Particle Swarm Optimization (PSO). The user can mix and match the three algorithms. For example, one can start optimization with either 2 or 3 and then use the optimized solution to further fine tune with approach 1. The secondary focus of this paper is to demonstrate the application of this tool to optimize/calibrate parameters for a nonlinear viscoplastic matrix to predict stress-strain curves (for constituent and composite levels) at different rates, temperatures and/or loading conditions utilizing the Generalized Method of Cells. After preliminary validation of the tool through comparison with experimental results, a detailed virtual parametric study is presented wherein the combined effects of temperature and loading rate on the predicted response of a braided composite is investigated.

Design of materials with prescribed nonlinear properties

NASA Astrophysics Data System (ADS)

Wang, F.; Sigmund, O.; Jensen, J. S.

2014-09-01

We systematically design materials using topology optimization to achieve prescribed nonlinear properties under finite deformation. Instead of a formal homogenization procedure, a numerical experiment is proposed to evaluate the material performance in longitudinal and transverse tensile tests under finite deformation, i.e. stress-strain relations and Poissons ratio. By minimizing errors between actual and prescribed properties, materials are tailored to achieve the target. Both two dimensional (2D) truss-based and continuum materials are designed with various prescribed nonlinear properties. The numerical examples illustrate optimized materials with rubber-like behavior and also optimized materials with extreme strain-independent Poissons ratio for axial strain intervals of εi∈[0.00, 0.30].

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Optimized System Identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Longman, Richard W.

1999-01-01

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Computer simulations of optimum boost and buck-boost converters

NASA Technical Reports Server (NTRS)

Rahman, S.

1982-01-01

The development of mathematicl models suitable for minimum weight boost and buck-boost converter designs are presented. The facility of an augumented Lagrangian (ALAG) multiplier-based nonlinear programming technique is demonstrated for minimum weight design optimizations of boost and buck-boost power converters. ALAG-based computer simulation results for those two minimum weight designs are discussed. Certain important features of ALAG are presented in the framework of a comprehensive design example for boost and buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight annd loss profiles of various semiconductor components and magnetics as a function of the switching frequency.

Structural dynamics analysis

NASA Technical Reports Server (NTRS)

Housner, J. M.; Anderson, M.; Belvin, W.; Horner, G.

1985-01-01

Dynamic analysis of large space antenna systems must treat the deployment as well as vibration and control of the deployed antenna. Candidate computer programs for deployment dynamics, and issues and needs for future program developments are reviewed. Some results for mast and hoop deployment are also presented. Modeling of complex antenna geometry with conventional finite element methods and with repetitive exact elements is considered. Analytical comparisons with experimental results for a 15 meter hoop/column antenna revealed the importance of accurate structural properties including nonlinear joints. Slackening of cables in this antenna is also a consideration. The technology of designing actively damped structures through analytical optimization is discussed and results are presented.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics.

PubMed

Egea, Jose A; Henriques, David; Cokelaer, Thomas; Villaverde, Alejandro F; MacNamara, Aidan; Danciu, Diana-Patricia; Banga, Julio R; Saez-Rodriguez, Julio

2014-05-10

Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools. We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html. Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods. MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics

PubMed Central

2014-01-01

Background Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools. Results We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html. Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods. Conclusions MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods. PMID:24885957

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.

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.

DYNA3D: A computer code for crashworthiness engineering

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

Hallquist, J.O.; Benson, D.J.

1986-09-01

A finite element program with crashworthiness applications has been developed at LLNL. DYNA3D, an explicit, fully vectorized, finite deformation structural dynamics program, has four capabilities that are critical for the efficient and realistic modeling crash phenomena: (1) fully optimized nonlinear solid, shell, and beam elements for representing a structure; (2) a broad range of constitutive models for simulating material behavior; (3) sophisticated contact algorithms for impact interactions; (4) a rigid body capability to represent the bodies away from the impact region at a greatly reduced cost without sacrificing accuracy in the momentum calculations. Basic methodologies of the program are brieflymore » presented along with several crashworthiness calculations. Efficiencies of the Hughes-Liu and Belytschko-Tsay shell formulations are considered.« less

Status report on the Aeronautical Research Institute of Sweden version of the missile aerodynamics program LARV, for calculation of static aerodynamic properties and longitudinal aerodynamic damping derivatives. Part 1: Theory

NASA Astrophysics Data System (ADS)

Weibust, E.

Improvements to a missile aerodynamics program which enable it to (a) calculate aerodynamic coefficients as input for a flight mechanics model, (b) check manufacturers' data or estimate performance from photographs, (c) reduce wind tunnel testing, and (d) aid optimization studies, are discussed. Slender body theory is used for longitudinal damping derivatives prediction. Program predictions were compared to known values. Greater accuracy is required in the estimation of drag due to excrescences on actual missile configurations, the influence of a burning motor, and nonlinear effects in the stall region. Prediction of pressure centers on wings and on bodies in presence of wings must be improved.

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).

Utility of coupling nonlinear optimization methods with numerical modeling software

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

Murphy, M.J.

1996-08-05

Results of using GLO (Global Local Optimizer), a general purpose nonlinear optimization software package for investigating multi-parameter problems in science and engineering is discussed. The package consists of the modular optimization control system (GLO), a graphical user interface (GLO-GUI), a pre-processor (GLO-PUT), a post-processor (GLO-GET), and nonlinear optimization software modules, GLOBAL & LOCAL. GLO is designed for controlling and easy coupling to any scientific software application. GLO runs the optimization module and scientific software application in an iterative loop. At each iteration, the optimization module defines new values for the set of parameters being optimized. GLO-PUT inserts the new parametermore » values into the input file of the scientific application. GLO runs the application with the new parameter values. GLO-GET determines the value of the objective function by extracting the results of the analysis and comparing to the desired result. GLO continues to run the scientific application over and over until it finds the ``best`` set of parameters by minimizing (or maximizing) the objective function. An example problem showing the optimization of material model is presented (Taylor cylinder impact test).« less

Fully localised nonlinear energy growth optimals in pipe flow

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

Pringle, Chris C. T.; Willis, Ashley P.; Kerswell, Rich R.

A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shearmore » flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust.« less

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

NASA Astrophysics Data System (ADS)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one step to any point in the near-optimal region, and each iterate generates a new, feasible alternative. We use the method to generate alternatives that span the near-optimal regions of simple and more complicated water management problems and may be preferred to optimal solutions. We also discuss extensions to handle non-linear equity constraints.

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.

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

1992-01-01

The papers presented at the symposium cover aerodynamics, design applications, propulsion systems, high-speed flight, structures, controls, sensitivity analysis, optimization algorithms, and space structures applications. Other topics include helicopter rotor design, artificial intelligence/neural nets, and computational aspects of optimization. Papers are included on flutter calculations for a system with interacting nonlinearities, optimization in solid rocket booster application, improving the efficiency of aerodynamic shape optimization procedures, nonlinear control theory, and probabilistic structural analysis of space truss structures for nonuniform thermal environmental effects.

Online optimization of storage ring nonlinear beam dynamics

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

Huang, Xiaobiao; Safranek, James

2015-08-01

We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short period of time. Experimental setup and results are presented.

New human-centered linear and nonlinear motion cueing algorithms for control of simulator motion systems

NASA Astrophysics Data System (ADS)

Telban, Robert J.

While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. To address this, new human-centered motion cueing algorithms were developed. A revised "optimal algorithm" uses time-invariant filters developed by optimal control, incorporating human vestibular system models. The "nonlinear algorithm" is a novel approach that is also formulated by optimal control, but can also be updated in real time. It incorporates a new integrated visual-vestibular perception model that includes both visual and vestibular sensation and the interaction between the stimuli. A time-varying control law requires the matrix Riccati equation to be solved in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. As a result of unsatisfactory sensation, an augmented turbulence cue was added to the vertical mode for both the optimal and nonlinear algorithms. The relative effectiveness of the algorithms, in simulating aircraft maneuvers, was assessed with an eleven-subject piloted performance test conducted on the NASA Langley Visual Motion Simulator (VMS). Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input analysis shows pilot-induced oscillations on a straight-in approach are less prevalent compared to the optimal algorithm. The augmented turbulence cues increased workload on an offset approach that the pilots deemed more realistic compared to the NASA adaptive algorithm. The takeoff with engine failure showed the least roll activity for the nonlinear algorithm, with the least rudder pedal activity for the optimal algorithm.

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.

Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.

2004-01-01

A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.

Research on theoretical optimization and experimental verification of minimum resistance hull form based on Rankine source method

NASA Astrophysics Data System (ADS)

Zhang, Bao-Ji; Zhang, Zhu-Xin

2015-09-01

To obtain low resistance and high efficiency energy-saving ship, minimum total resistance hull form design method is studied based on potential flow theory of wave-making resistance and considering the effects of tail viscous separation. With the sum of wave resistance and viscous resistance as objective functions and the parameters of B-Spline function as design variables, mathematical models are built using Nonlinear Programming Method (NLP) ensuring the basic limit of displacement and considering rear viscous separation. We develop ship lines optimization procedures with intellectual property rights. Series60 is used as parent ship in optimization design to obtain improved ship (Series60-1) theoretically. Then drag tests for the improved ship (Series60-1) is made to get the actual minimum total resistance hull form.

Analysis of point-to-point lung motion with full inspiration and expiration CT data using non-linear optimization method: optimal geometric assumption model for the effective registration algorithm

NASA Astrophysics Data System (ADS)

Kim, Namkug; Seo, Joon Beom; Heo, Jeong Nam; Kang, Suk-Ho

2007-03-01

The study was conducted to develop a simple model for more robust lung registration of volumetric CT data, which is essential for various clinical lung analysis applications, including the lung nodule matching in follow up CT studies, semi-quantitative assessment of lung perfusion, and etc. The purpose of this study is to find the most effective reference point and geometric model based on the lung motion analysis from the CT data sets obtained in full inspiration (In.) and expiration (Ex.). Ten pairs of CT data sets in normal subjects obtained in full In. and Ex. were used in this study. Two radiologists were requested to draw 20 points representing the subpleural point of the central axis in each segment. The apex, hilar point, and center of inertia (COI) of each unilateral lung were proposed as the reference point. To evaluate optimal expansion point, non-linear optimization without constraints was employed. The objective function is sum of distances from the line, consist of the corresponding points between In. and Ex. to the optimal point x. By using the nonlinear optimization, the optimal points was evaluated and compared between reference points. The average distance between the optimal point and each line segment revealed that the balloon model was more suitable to explain the lung expansion model. This lung motion analysis based on vector analysis and non-linear optimization shows that balloon model centered on the center of inertia of lung is most effective geometric model to explain lung expansion by breathing.

Multi-objective possibilistic model for portfolio selection with transaction cost

NASA Astrophysics Data System (ADS)

Jana, P.; Roy, T. K.; Mazumder, S. K.

2009-06-01

In this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples.

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

PubMed

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

2013-12-01

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

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems

NASA Astrophysics Data System (ADS)

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

2011-08-01

This paper proposes a novel optimization approach for the least cost design of looped water distribution systems (WDSs). Three distinct steps are involved in the proposed optimization approach. In the first step, the shortest-distance tree within the looped network is identified using the Dijkstra graph theory algorithm, for which an extension is proposed to find the shortest-distance tree for multisource WDSs. In the second step, a nonlinear programming (NLP) solver is employed to optimize the pipe diameters for the shortest-distance tree (chords of the shortest-distance tree are allocated the minimum allowable pipe sizes). Finally, in the third step, the original looped water network is optimized using a differential evolution (DE) algorithm seeded with diameters in the proximity of the continuous pipe sizes obtained in step two. As such, the proposed optimization approach combines the traditional deterministic optimization technique of NLP with the emerging evolutionary algorithm DE via the proposed network decomposition. The proposed methodology has been tested on four looped WDSs with the number of decision variables ranging from 21 to 454. Results obtained show the proposed approach is able to find optimal solutions with significantly less computational effort than other optimization techniques.

Analytical and Computational Properties of Distributed Approaches to MDO

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia M.; Lewis, Robert Michael

2000-01-01

Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis

Interactive optimization approach for optimal impulsive rendezvous using primer vector and evolutionary algorithms

NASA Astrophysics Data System (ADS)

Luo, Ya-Zhong; Zhang, Jin; Li, Hai-yang; Tang, Guo-Jin

2010-08-01

In this paper, a new optimization approach combining primer vector theory and evolutionary algorithms for fuel-optimal non-linear impulsive rendezvous is proposed. The optimization approach is designed to seek the optimal number of impulses as well as the optimal impulse vectors. In this optimization approach, adding a midcourse impulse is determined by an interactive method, i.e. observing the primer-magnitude time history. An improved version of simulated annealing is employed to optimize the rendezvous trajectory with the fixed-number of impulses. This interactive approach is evaluated by three test cases: coplanar circle-to-circle rendezvous, same-circle rendezvous and non-coplanar rendezvous. The results show that the interactive approach is effective and efficient in fuel-optimal non-linear rendezvous design. It can guarantee solutions, which satisfy the Lawden's necessary optimality conditions.

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

Nonlinear Model Predictive Control for Cooperative Control and Estimation

NASA Astrophysics Data System (ADS)

Ru, Pengkai

Recent advances in computational power have made it possible to do expensive online computations for control systems. It is becoming more realistic to perform computationally intensive optimization schemes online on systems that are not intrinsically stable and/or have very small time constants. Being one of the most important optimization based control approaches, model predictive control (MPC) has attracted a lot of interest from the research community due to its natural ability to incorporate constraints into its control formulation. Linear MPC has been well researched and its stability can be guaranteed in the majority of its application scenarios. However, one issue that still remains with linear MPC is that it completely ignores the system's inherent nonlinearities thus giving a sub-optimal solution. On the other hand, if achievable, nonlinear MPC, would naturally yield a globally optimal solution and take into account all the innate nonlinear characteristics. While an exact solution to a nonlinear MPC problem remains extremely computationally intensive, if not impossible, one might wonder if there is a middle ground between the two. We tried to strike a balance in this dissertation by employing a state representation technique, namely, the state dependent coefficient (SDC) representation. This new technique would render an improved performance in terms of optimality compared to linear MPC while still keeping the problem tractable. In fact, the computational power required is bounded only by a constant factor of the completely linearized MPC. The purpose of this research is to provide a theoretical framework for the design of a specific kind of nonlinear MPC controller and its extension into a general cooperative scheme. The controller is designed and implemented on quadcopter systems.

Nonlinear Motion Cueing Algorithm: Filtering at Pilot Station and Development of the Nonlinear Optimal Filters for Pitch and Roll

NASA Technical Reports Server (NTRS)

Zaychik, Kirill B.; Cardullo, Frank M.

2012-01-01

Telban and Cardullo have developed and successfully implemented the non-linear optimal motion cueing algorithm at the Visual Motion Simulator (VMS) at the NASA Langley Research Center in 2005. The latest version of the non-linear algorithm performed filtering of motion cues in all degrees-of-freedom except for pitch and roll. This manuscript describes the development and implementation of the non-linear optimal motion cueing algorithm for the pitch and roll degrees of freedom. Presented results indicate improved cues in the specified channels as compared to the original design. To further advance motion cueing in general, this manuscript describes modifications to the existing algorithm, which allow for filtering at the location of the pilot's head as opposed to the centroid of the motion platform. The rational for such modification to the cueing algorithms is that the location of the pilot's vestibular system must be taken into account as opposed to the off-set of the centroid of the cockpit relative to the center of rotation alone. Results provided in this report suggest improved performance of the motion cueing algorithm.

The solution of private problems for optimization heat exchangers parameters

NASA Astrophysics Data System (ADS)

Melekhin, A.

2017-11-01

The relevance of the topic due to the decision of problems of the economy of resources in heating systems of buildings. To solve this problem we have developed an integrated method of research which allows solving tasks on optimization of parameters of heat exchangers. This method decides multicriteria optimization problem with the program nonlinear optimization on the basis of software with the introduction of an array of temperatures obtained using thermography. The author have developed a mathematical model of process of heat exchange in heat exchange surfaces of apparatuses with the solution of multicriteria optimization problem and check its adequacy to the experimental stand in the visualization of thermal fields, an optimal range of managed parameters influencing the process of heat exchange with minimal metal consumption and the maximum heat output fin heat exchanger, the regularities of heat exchange process with getting generalizing dependencies distribution of temperature on the heat-release surface of the heat exchanger vehicles, defined convergence of the results of research in the calculation on the basis of theoretical dependencies and solving mathematical model.

Multidisciplinary design optimization using multiobjective formulation techniques

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Pagaldipti, Narayanan S.

1995-01-01

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Optimal Operation System of the Integrated District Heating System with Multiple Regional Branches

NASA Astrophysics Data System (ADS)

Kim, Ui Sik; Park, Tae Chang; Kim, Lae-Hyun; Yeo, Yeong Koo

This paper presents an optimal production and distribution management for structural and operational optimization of the integrated district heating system (DHS) with multiple regional branches. A DHS consists of energy suppliers and consumers, district heating pipelines network and heat storage facilities in the covered region. In the optimal management system, production of heat and electric power, regional heat demand, electric power bidding and sales, transport and storage of heat at each regional DHS are taken into account. The optimal management system is formulated as a mixed integer linear programming (MILP) where the objectives is to minimize the overall cost of the integrated DHS while satisfying the operation constraints of heat units and networks as well as fulfilling heating demands from consumers. Piecewise linear formulation of the production cost function and stairwise formulation of the start-up cost function are used to compute nonlinear cost function approximately. Evaluation of the total overall cost is based on weekly operations at each district heat branches. Numerical simulations show the increase of energy efficiency due to the introduction of the present optimal management system.

Adaptive adjustment of interval predictive control based on combined model and application in shell brand petroleum distillation tower

NASA Astrophysics Data System (ADS)

Sun, Chao; Zhang, Chunran; Gu, Xinfeng; Liu, Bin

2017-10-01

Constraints of the optimization objective are often unable to be met when predictive control is applied to industrial production process. Then, online predictive controller will not find a feasible solution or a global optimal solution. To solve this problem, based on Back Propagation-Auto Regressive with exogenous inputs (BP-ARX) combined control model, nonlinear programming method is used to discuss the feasibility of constrained predictive control, feasibility decision theorem of the optimization objective is proposed, and the solution method of soft constraint slack variables is given when the optimization objective is not feasible. Based on this, for the interval control requirements of the controlled variables, the slack variables that have been solved are introduced, the adaptive weighted interval predictive control algorithm is proposed, achieving adaptive regulation of the optimization objective and automatically adjust of the infeasible interval range, expanding the scope of the feasible region, and ensuring the feasibility of the interval optimization objective. Finally, feasibility and effectiveness of the algorithm is validated through the simulation comparative experiments.

NOLIN: A nonlinear laminate analysis program

NASA Technical Reports Server (NTRS)

Kibler, J. J.

1975-01-01

A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

Slave finite element for non-linear analysis of engine structures. Volume 2: Programmer's manual and user's manual

NASA Technical Reports Server (NTRS)

Witkop, D. L.; Dale, B. J.; Gellin, S.

1991-01-01

The programming aspects of SFENES are described in the User's Manual. The information presented is provided for the installation programmer. It is sufficient to fully describe the general program logic and required peripheral storage. All element generated data is stored externally to reduce required memory allocation. A separate section is devoted to the description of these files thereby permitting the optimization of Input/Output (I/O) time through efficient buffer descriptions. Individual subroutine descriptions are presented along with the complete Fortran source listings. A short description of the major control, computation, and I/O phases is included to aid in obtaining an overall familiarity with the program's components. Finally, a discussion of the suggested overlay structure which allows the program to execute with a reasonable amount of memory allocation is presented.

Embedded algorithms within an FPGA-based system to process nonlinear time series data

NASA Astrophysics Data System (ADS)

Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.

2008-03-01

This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better computational and power efficiency.

Optimizing basin-scale coupled water quantity and water quality man-agement with stochastic dynamic programming

NASA Astrophysics Data System (ADS)

Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Engelund Holm, Peter; Trapp, Stefan; Rosbjerg, Dan; Bauer-Gottwein, Peter

2015-04-01

Few studies address water quality in hydro-economic models, which often focus primarily on optimal allocation of water quantities. Water quality and water quantity are closely coupled, and optimal management with focus solely on either quantity or quality may cause large costs in terms of the oth-er component. In this study, we couple water quality and water quantity in a joint hydro-economic catchment-scale optimization problem. Stochastic dynamic programming (SDP) is used to minimize the basin-wide total costs arising from water allocation, water curtailment and water treatment. The simple water quality module can handle conservative pollutants, first order depletion and non-linear reactions. For demonstration purposes, we model pollutant releases as biochemical oxygen demand (BOD) and use the Streeter-Phelps equation for oxygen deficit to compute the resulting min-imum dissolved oxygen concentrations. Inelastic water demands, fixed water allocation curtailment costs and fixed wastewater treatment costs (before and after use) are estimated for the water users (agriculture, industry and domestic). If the BOD concentration exceeds a given user pollution thresh-old, the user will need to pay for pre-treatment of the water before use. Similarly, treatment of the return flow can reduce the BOD load to the river. A traditional SDP approach is used to solve one-step-ahead sub-problems for all combinations of discrete reservoir storage, Markov Chain inflow clas-ses and monthly time steps. Pollution concentration nodes are introduced for each user group and untreated return flow from the users contribute to increased BOD concentrations in the river. The pollutant concentrations in each node depend on multiple decision variables (allocation and wastewater treatment) rendering the objective function non-linear. Therefore, the pollution concen-tration decisions are outsourced to a genetic algorithm, which calls a linear program to determine the remainder of the decision variables. This hybrid formulation keeps the optimization problem computationally feasible and represents a flexible and customizable method. The method has been applied to the Ziya River basin, an economic hotspot located on the North China Plain in Northern China. The basin is subject to severe water scarcity, and the rivers are heavily polluted with wastewater and nutrients from diffuse sources. The coupled hydro-economic optimiza-tion model can be used to assess costs of meeting additional constraints such as minimum water qual-ity or to economically prioritize investments in waste water treatment facilities based on economic criteria.

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

1977-01-01

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

Modeling and Analysis of Power Processing Systems (MAPPS), initial phase 2

NASA Technical Reports Server (NTRS)

Yu, Y.; Lee, F. C.; Wangenheim, H.; Warren, D.

1977-01-01

The overall objective of the program is to provide the engineering tools to reduce the analysis, design, and development effort, and thus the cost, in achieving the required performances for switching regulators and dc-dc converter systems. The program was both tutorial and application oriented. Various analytical methods were described in detail and supplemented with examples, and those with standardization appeals were reduced into computer-based subprograms. Major program efforts included those concerning small and large signal control-dependent performance analysis and simulation, control circuit design, power circuit design and optimization, system configuration study, and system performance simulation. Techniques including discrete time domain, conventional frequency domain, Lagrange multiplier, nonlinear programming, and control design synthesis were employed in these efforts. To enhance interactive conversation between the modeling and analysis subprograms and the user, a working prototype of the Data Management Program was also developed to facilitate expansion as future subprogram capabilities increase.

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

NASA Astrophysics Data System (ADS)

Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

2015-04-01

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.

Estimation of in-situ bioremediation system cost using a hybrid Extreme Learning Machine (ELM)-particle swarm optimization approach

NASA Astrophysics Data System (ADS)

Yadav, Basant; Ch, Sudheer; Mathur, Shashi; Adamowski, Jan

2016-12-01

In-situ bioremediation is the most common groundwater remediation procedure used for treating organically contaminated sites. A simulation-optimization approach, which incorporates a simulation model for groundwaterflow and transport processes within an optimization program, could help engineers in designing a remediation system that best satisfies management objectives as well as regulatory constraints. In-situ bioremediation is a highly complex, non-linear process and the modelling of such a complex system requires significant computational exertion. Soft computing techniques have a flexible mathematical structure which can generalize complex nonlinear processes. In in-situ bioremediation management, a physically-based model is used for the simulation and the simulated data is utilized by the optimization model to optimize the remediation cost. The recalling of simulator to satisfy the constraints is an extremely tedious and time consuming process and thus there is need for a simulator which can reduce the computational burden. This study presents a simulation-optimization approach to achieve an accurate and cost effective in-situ bioremediation system design for groundwater contaminated with BTEX (Benzene, Toluene, Ethylbenzene, and Xylenes) compounds. In this study, the Extreme Learning Machine (ELM) is used as a proxy simulator to replace BIOPLUME III for the simulation. The selection of ELM is done by a comparative analysis with Artificial Neural Network (ANN) and Support Vector Machine (SVM) as they were successfully used in previous studies of in-situ bioremediation system design. Further, a single-objective optimization problem is solved by a coupled Extreme Learning Machine (ELM)-Particle Swarm Optimization (PSO) technique to achieve the minimum cost for the in-situ bioremediation system design. The results indicate that ELM is a faster and more accurate proxy simulator than ANN and SVM. The total cost obtained by the ELM-PSO approach is held to a minimum while successfully satisfying all the regulatory constraints of the contaminated site.

Topology optimization of hyperelastic structures using a level set method

NASA Astrophysics Data System (ADS)

Chen, Feifei; Wang, Yiqiang; Wang, Michael Yu; Zhang, Y. F.

2017-12-01

Soft rubberlike materials, due to their inherent compliance, are finding widespread implementation in a variety of applications ranging from assistive wearable technologies to soft material robots. Structural design of such soft and rubbery materials necessitates the consideration of large nonlinear deformations and hyperelastic material models to accurately predict their mechanical behaviour. In this paper, we present an effective level set-based topology optimization method for the design of hyperelastic structures that undergo large deformations. The method incorporates both geometric and material nonlinearities where the strain and stress measures are defined within the total Lagrange framework and the hyperelasticity is characterized by the widely-adopted Mooney-Rivlin material model. A shape sensitivity analysis is carried out, in the strict sense of the material derivative, where the high-order terms involving the displacement gradient are retained to ensure the descent direction. As the design velocity enters into the shape derivative in terms of its gradient and divergence terms, we develop a discrete velocity selection strategy. The whole optimization implementation undergoes a two-step process, where the linear optimization is first performed and its optimized solution serves as the initial design for the subsequent nonlinear optimization. It turns out that this operation could efficiently alleviate the numerical instability and facilitate the optimization process. To demonstrate the validity and effectiveness of the proposed method, three compliance minimization problems are studied and their optimized solutions present significant mechanical benefits of incorporating the nonlinearities, in terms of remarkable enhancement in not only the structural stiffness but also the critical buckling load.

Nonlinear optical microscopy for immunoimaging: a custom optimized system of high-speed, large-area, multicolor imaging

PubMed Central

Li, Hui; Cui, Quan; Zhang, Zhihong; Luo, Qingming

2015-01-01

Background The nonlinear optical microscopy has become the current state-of-the-art for intravital imaging. Due to its advantages of high resolution, superior tissue penetration, lower photodamage and photobleaching, as well as intrinsic z-sectioning ability, this technology has been widely applied in immunoimaging for a decade. However, in terms of monitoring immune events in native physiological environment, the conventional nonlinear optical microscope system has to be optimized for live animal imaging. Generally speaking, three crucial capabilities are desired, including high-speed, large-area and multicolor imaging. Among numerous high-speed scanning mechanisms used in nonlinear optical imaging, polygon scanning is not only linearly but also dispersion-freely with high stability and tunable rotation speed, which can overcome disadvantages of multifocal scanning, resonant scanner and acousto-optical deflector (AOD). However, low frame rate, lacking large-area or multicolor imaging ability make current polygonbased nonlinear optical microscopes unable to meet the requirements of immune event monitoring. Methods We built up a polygon-based nonlinear optical microscope system which was custom optimized for immunoimaging with high-speed, large-are and multicolor imaging abilities. Results Firstly, we validated the imaging performance of the system by standard methods. Then, to demonstrate the ability to monitor immune events, migration of immunocytes observed by the system based on typical immunological models such as lymph node, footpad and dorsal skinfold chamber are shown. Finally, we take an outlook for the possible advance of related technologies such as sample stabilization and optical clearing for more stable and deeper intravital immunoimaging. Conclusions This study will be helpful for optimizing nonlinear optical microscope to obtain more comprehensive and accurate information of immune events. PMID:25694951

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Analytical Optimization of the Net Residual Dispersion in SPM-Limited Dispersion-Managed Systems

NASA Astrophysics Data System (ADS)

Xiao, Xiaosheng; Gao, Shiming; Tian, Yu; Yang, Changxi

2006-05-01

Dispersion management is an effective technique to suppress the nonlinear impairment in fiber transmission systems, which includes tuning the amounts of precompensation, residual dispersion per span (RDPS), and net residual dispersion (NRD) of the systems. For self-phase modulation (SPM)-limited systems, optimizing the NRD is necessary because it can greatly improve the system performance. In this paper, an analytical method is presented to optimize NRD for SPM-limited dispersion-managed systems. The method is based on the correlation between the nonlinear impairment and the output pulse broadening of SPM-limited systems; therefore, dispersion-managed systems can be optimized through minimizing the output single-pulse broadening. A set of expressions is derived to calculate the output pulse broadening of the SPM-limited dispersion-managed system, from which the analytical result of optimal NRD is obtained. Furthermore, with the expressions of pulse broadening, how the nonlinear impairment depends on the amounts of precompensation and RDPS can be revealed conveniently.

The Efficiency of Split Panel Designs in an Analysis of Variance Model

PubMed Central

Wang, Wei-Guo; Liu, Hai-Jun

2016-01-01

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution. PMID:27163447

Robust attitude control design for spacecraft under assigned velocity and control constraints.

PubMed

Hu, Qinglei; Li, Bo; Zhang, Youmin

2013-07-01

A novel robust nonlinear control design under the constraints of assigned velocity and actuator torque is investigated for attitude stabilization of a rigid spacecraft. More specifically, a nonlinear feedback control is firstly developed by explicitly taking into account the constraints on individual angular velocity components as well as external disturbances. Considering further the actuator misalignments and magnitude deviation, a modified robust least-squares based control allocator is employed to deal with the problem of distributing the previously designed three-axis moments over the available actuators, in which the focus of this control allocation is to find the optimal control vector of actuators by minimizing the worst-case residual error using programming algorithms. The attitude control performance using the controller structure is evaluated through a numerical example. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Bio-inspired computational heuristics to study Lane-Emden systems arising in astrophysics model.

PubMed

Ahmad, Iftikhar; Raja, Muhammad Asif Zahoor; Bilal, Muhammad; Ashraf, Farooq

2016-01-01

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.

An adaptive critic-based scheme for consensus control of nonlinear multi-agent systems

NASA Astrophysics Data System (ADS)

Heydari, Ali; Balakrishnan, S. N.

2014-12-01

The problem of decentralised consensus control of a network of heterogeneous nonlinear systems is formulated as an optimal tracking problem and a solution is proposed using an approximate dynamic programming based neurocontroller. The neurocontroller training comprises an initial offline training phase and an online re-optimisation phase to account for the fact that the reference signal subject to tracking is not fully known and available ahead of time, i.e., during the offline training phase. As long as the dynamics of the agents are controllable, and the communication graph has a directed spanning tree, this scheme guarantees the synchronisation/consensus even under switching communication topology and directed communication graph. Finally, an aerospace application is selected for the evaluation of the performance of the method. Simulation results demonstrate the potential of the scheme.

GOSA, a simulated annealing-based program for global optimization of nonlinear problems, also reveals transyears

PubMed Central

Czaplicki, Jerzy; Cornélissen, Germaine; Halberg, Franz

2009-01-01

Summary Transyears in biology have been documented thus far by the extended cosinor approach, including linear-nonlinear rhythmometry. We here confirm the existence of transyears by simulated annealing, a method originally developed for a much broader use, but described and introduced herein for validating its application to time series. The method is illustrated both on an artificial test case with known components and on biological data. We provide a table comparing results by the two methods and trust that the procedure will serve the budding sciences of chronobiology (the study of mechanisms underlying biological time structure), chronomics (the mapping of time structures in and around us), and chronobioethics, using the foregoing disciplines to add to concern for illnesses of individuals, and to budding focus on diseases of nations and civilizations. PMID:20414480

A non-linear optimization programming model for air quality planning including co-benefits for GHG emissions.

PubMed

Turrini, Enrico; Carnevale, Claudio; Finzi, Giovanna; Volta, Marialuisa

2018-04-15

This paper introduces the MAQ (Multi-dimensional Air Quality) model aimed at defining cost-effective air quality plans at different scales (urban to national) and assessing the co-benefits for GHG emissions. The model implements and solves a non-linear multi-objective, multi-pollutant decision problem where the decision variables are the application levels of emission abatement measures allowing the reduction of energy consumption, end-of pipe technologies and fuel switch options. The objectives of the decision problem are the minimization of tropospheric secondary pollution exposure and of internal costs. The model assesses CO 2 equivalent emissions in order to support decision makers in the selection of win-win policies. The methodology is tested on Lombardy region, a heavily polluted area in northern Italy. Copyright © 2017 Elsevier B.V. All rights reserved.

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

A Nonlinear Fuel Optimal Reaction Jet Control Law

DTIC Science & Technology

2002-07-29

derive a nonlinear fuel optimal attitude control system (ACS) that drives the final state to the desired state according to a cost function that...αroll = 0.22 rad/s2 and αyaw = 0.20 rad/s2. [ ] ( )( )ωωτω rrr&r r&r ⋅×−⋅= ⋅Ω−= − 2 1 1 II QQ (9) where, Q r is the attitude quaternion ...from Table-1 regarding the relative performance of the nonlinear controller with a conventional PID controller ( used in this paper as a benchmark for

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun Yuan; Young, D. H.

1991-01-01

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

NASA Astrophysics Data System (ADS)

Fowler, J. W.; Pappas, C. G.; Alpert, B. K.; Doriese, W. B.; O'Neil, G. C.; Ullom, J. N.; Swetz, D. S.

2018-03-01

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of linear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.

Optimal signal constellation design for ultra-high-speed optical transport in the presence of nonlinear phase noise.

PubMed

Liu, Tao; Djordjevic, Ivan B

2014-12-29

In this paper, we first describe an optimal signal constellation design algorithm suitable for the coherent optical channels dominated by the linear phase noise. Then, we modify this algorithm to be suitable for the nonlinear phase noise dominated channels. In optimization procedure, the proposed algorithm uses the cumulative log-likelihood function instead of the Euclidian distance. Further, an LDPC coded modulation scheme is proposed to be used in combination with signal constellations obtained by proposed algorithm. Monte Carlo simulations indicate that the LDPC-coded modulation schemes employing the new constellation sets, obtained by our new signal constellation design algorithm, outperform corresponding QAM constellations significantly in terms of transmission distance and have better nonlinearity tolerance.

Cocontraction of pairs of antagonistic muscles: analytical solution for planar static nonlinear optimization approaches.

PubMed

Herzog, W; Binding, P

1993-11-01

It has been stated in the literature that static, nonlinear optimization approaches cannot predict coactivation of pairs of antagonistic muscles; however, numerical solutions of such approaches have predicted coactivation of pairs of one-joint and multijoint antagonists. Analytical support for either finding is not available in the literature for systems containing more than one degree of freedom. The purpose of this study was to investigate analytically the possibility of cocontraction of pairs of antagonistic muscles using a static nonlinear optimization approach for a multidegree-of-freedom, two-dimensional system. Analytical solutions were found using the Karush-Kuhn-Tucker conditions, which were necessary and sufficient for optimality in this problem. The results show that cocontraction of pairs of one-joint antagonistic muscles is not possible, whereas cocontraction of pairs of multijoint antagonists is. These findings suggest that cocontraction of pairs of antagonistic muscles may be an "efficient" way to accomplish many movement tasks.

Analysis of the faster-than-Nyquist optimal linear multicarrier system

NASA Astrophysics Data System (ADS)

Marquet, Alexandre; Siclet, Cyrille; Roque, Damien

2017-02-01

Faster-than-Nyquist signalization enables a better spectral efficiency at the expense of an increased computational complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization of the linear part of the system. In this article, we analyze the performance of the optimal linear multicarrier system when used together with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the normality assumption of the interference, used for implementing such non-linear systems. The use of this optimal linear system leads to a closed-form expression of the bit-error probability that can be used to predict the performance and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context. xml:lang="fr"

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

NASA Astrophysics Data System (ADS)

Yang, Xiong; Liu, Derong; Wang, Ding

2014-03-01

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

Comparisons of linear and nonlinear pyramid schemes for signal and image processing

NASA Astrophysics Data System (ADS)

Morales, Aldo W.; Ko, Sung-Jea

1997-04-01

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

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

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is notmore » assumed that the iterates lie on a compact set.« less

A multiobjective optimization framework for multicontaminant industrial water network design.

PubMed

Boix, Marianne; Montastruc, Ludovic; Pibouleau, Luc; Azzaro-Pantel, Catherine; Domenech, Serge

2011-07-01

The optimal design of multicontaminant industrial water networks according to several objectives is carried out in this paper. The general formulation of the water allocation problem (WAP) is given as a set of nonlinear equations with binary variables representing the presence of interconnections in the network. For optimization purposes, three antagonist objectives are considered: F(1), the freshwater flow-rate at the network entrance, F(2), the water flow-rate at inlet of regeneration units, and F(3), the number of interconnections in the network. The multiobjective problem is solved via a lexicographic strategy, where a mixed-integer nonlinear programming (MINLP) procedure is used at each step. The approach is illustrated by a numerical example taken from the literature involving five processes, one regeneration unit and three contaminants. The set of potential network solutions is provided in the form of a Pareto front. Finally, the strategy for choosing the best network solution among those given by Pareto fronts is presented. This Multiple Criteria Decision Making (MCDM) problem is tackled by means of two approaches: a classical TOPSIS analysis is first implemented and then an innovative strategy based on the global equivalent cost (GEC) in freshwater that turns out to be more efficient for choosing a good network according to a practical point of view. Copyright © 2011 Elsevier Ltd. All rights reserved.

Robust/optimal temperature profile control of a high-speed aerospace vehicle using neural networks.

PubMed

Yadav, Vivek; Padhi, Radhakant; Balakrishnan, S N

2007-07-01

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A 1-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

NLINEAR - NONLINEAR CURVE FITTING PROGRAM

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1994-01-01

A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Nonlinear optimal filter technique for analyzing energy depositions in TES sensors driven into saturation

DOE PAGES

Shank, B.; Yen, J. J.; Cabrera, B.; ...

2014-11-04

We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs) connected to quasiparticle (qp) traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search) Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.

PSC algorithm description

NASA Technical Reports Server (NTRS)

Nobbs, Steven G.

1995-01-01

An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.

Evidence of soft bound behaviour in analogue memristive devices for neuromorphic computing.

PubMed

Frascaroli, Jacopo; Brivio, Stefano; Covi, Erika; Spiga, Sabina

2018-05-08

The development of devices that can modulate their conductance under the application of electrical stimuli constitutes a fundamental step towards the realization of synaptic connectivity in neural networks. Optimization of synaptic functionality requires the understanding of the analogue conductance update under different programming conditions. Moreover, properties of physical devices such as bounded conductance values and state-dependent modulation should be considered as they affect storage capacity and performance of the network. This work provides a study of the conductance dynamics produced by identical pulses as a function of the programming parameters in an HfO 2 memristive device. The application of a phenomenological model that considers a soft approach to the conductance boundaries allows the identification of different operation regimes and to quantify conductance modulation in the analogue region. Device non-linear switching kinetics is recognized as the physical origin of the transition between different dynamics and motivates the crucial trade-off between degree of analog modulation and memory window. Different kinetics for the processes of conductance increase and decrease account for device programming asymmetry. The identification of programming trade-off together with an evaluation of device variations provide a guideline for the optimization of the analogue programming in view of hardware implementation of neural networks.

Distributed mixed-integer fuzzy hierarchical programming for municipal solid waste management. Part I: System identification and methodology development.

PubMed

Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Xiujuan; Chen, Jiapei

2017-03-01

Due to the existence of complexities of heterogeneities, hierarchy, discreteness, and interactions in municipal solid waste management (MSWM) systems such as Beijing, China, a series of socio-economic and eco-environmental problems may emerge or worsen and result in irredeemable damages in the following decades. Meanwhile, existing studies, especially ones focusing on MSWM in Beijing, could hardly reflect these complexities in system simulations and provide reliable decision support for management practices. Thus, a framework of distributed mixed-integer fuzzy hierarchical programming (DMIFHP) is developed in this study for MSWM under these complexities. Beijing is selected as a representative case. The Beijing MSWM system is comprehensively analyzed in many aspects such as socio-economic conditions, natural conditions, spatial heterogeneities, treatment facilities, and system complexities, building a solid foundation for system simulation and optimization. Correspondingly, the MSWM system in Beijing is discretized as 235 grids to reflect spatial heterogeneity. A DMIFHP model which is a nonlinear programming problem is constructed to parameterize the Beijing MSWM system. To enable scientific solving of it, a solution algorithm is proposed based on coupling of fuzzy programming and mixed-integer linear programming. Innovations and advantages of the DMIFHP framework are discussed. The optimal MSWM schemes and mechanism revelations will be discussed in another companion paper due to length limitation.

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

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

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

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

Supersonic civil airplane study and design: Performance and sonic boom

NASA Technical Reports Server (NTRS)

Cheung, Samson

1995-01-01

Since aircraft configuration plays an important role in aerodynamic performance and sonic boom shape, the configuration of the next generation supersonic civil transport has to be tailored to meet high aerodynamic performance and low sonic boom requirements. Computational fluid dynamics (CFD) can be used to design airplanes to meet these dual objectives. The work and results in this report are used to support NASA's High Speed Research Program (HSRP). CFD tools and techniques have been developed for general usages of sonic boom propagation study and aerodynamic design. Parallel to the research effort on sonic boom extrapolation, CFD flow solvers have been coupled with a numeric optimization tool to form a design package for aircraft configuration. This CFD optimization package has been applied to configuration design on a low-boom concept and an oblique all-wing concept. A nonlinear unconstrained optimizer for Parallel Virtual Machine has been developed for aerodynamic design and study.

Energy-modeled flight in a wind field

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

Feldman, M.A.; Cliff, E.M.

Optimal shaping of aerospace trajectories has provided the motivation for much modern study of optimization theory and algorithms. Current industrial practice favors approaches where the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP) by a discretization process. Two such formulations are implemented in the POST and the OTIS codes. In the present paper we use a discretization that is specially adapted to the flight problem of interest. Among the unique aspects of the present discretization are: a least-squares formulation for certain kinematic constraints; the use of an energy ideas to enforce Newton`s Laws; and, themore » inclusion of large magnitude horizontal winds. In the next section we shall provide a description of the flight problem and its NLP representation. Following this we provide some details of the constraint formulation. Finally, we present an overview of the NLP problem.« less

Optimal design of zero-water discharge rinsing systems.

PubMed

Thöming, Jorg

2002-03-01

This paper is about zero liquid discharge in processes that use water for rinsing. Emphasis was given to those systems that contaminate process water with valuable process liquor and compounds. The approach involved the synthesis of optimal rinsing and recycling networks (RRN) that had a priori excluded water discharge. The total annualized costs of the RRN were minimized by the use of a mixed-integer nonlinear program (MINLP). This MINLP was based on a hyperstructure of the RRN and contained eight counterflow rinsing stages and three regenerator units: electrodialysis, reverse osmosis, and ion exchange columns. A "large-scale nickel plating process" case study showed that by means of zero-water discharge and optimized rinsing the total waste could be reduced by 90.4% at a revenue of $448,000/yr. Furthermore, with the optimized RRN, the rinsing performance can be improved significantly at a low-cost increase. In all the cases, the amount of valuable compounds reclaimed was above 99%.

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1995-01-01

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

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.

Multi-input multioutput orthogonal frequency division multiplexing radar waveform design for improving the detection performance of space-time adaptive processing

NASA Astrophysics Data System (ADS)

Wang, Hongyan

2017-04-01

This paper addresses the waveform optimization problem for improving the detection performance of multi-input multioutput (MIMO) orthogonal frequency division multiplexing (OFDM) radar-based space-time adaptive processing (STAP) in the complex environment. By maximizing the output signal-to-interference-and-noise-ratio (SINR) criterion, the waveform optimization problem for improving the detection performance of STAP, which is subjected to the constant modulus constraint, is derived. To tackle the resultant nonlinear and complicated optimization issue, a diagonal loading-based method is proposed to reformulate the issue as a semidefinite programming one; thereby, this problem can be solved very efficiently. In what follows, the optimized waveform can be obtained to maximize the output SINR of MIMO-OFDM such that the detection performance of STAP can be improved. The simulation results show that the proposed method can improve the output SINR detection performance considerably as compared with that of uncorrelated waveforms and the existing MIMO-based STAP method.

AITSO: A Tool for Spatial Optimization Based on Artificial Immune Systems

PubMed Central

Zhao, Xiang; Liu, Yaolin; Liu, Dianfeng; Ma, Xiaoya

2015-01-01

A great challenge facing geocomputation and spatial analysis is spatial optimization, given that it involves various high-dimensional, nonlinear, and complicated relationships. Many efforts have been made with regard to this specific issue, and the strong ability of artificial immune system algorithms has been proven in previous studies. However, user-friendly professional software is still unavailable, which is a great impediment to the popularity of artificial immune systems. This paper describes a free, universal tool, named AITSO, which is capable of solving various optimization problems. It provides a series of standard application programming interfaces (APIs) which can (1) assist researchers in the development of their own problem-specific application plugins to solve practical problems and (2) allow the implementation of some advanced immune operators into the platform to improve the performance of an algorithm. As an integrated, flexible, and convenient tool, AITSO contributes to knowledge sharing and practical problem solving. It is therefore believed that it will advance the development and popularity of spatial optimization in geocomputation and spatial analysis. PMID:25678911

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

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-09-07

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

Early seizure detection in an animal model of temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

Talathi, Sachin S.; Hwang, Dong-Uk; Ditto, William; Carney, Paul R.

2007-11-01

The performance of five seizure detection schemes, i.e., Nonlinear embedding delay, Hurst scaling, Wavelet Scale, autocorrelation and gradient of accumulated energy, in their ability to detect EEG seizures close to the seizure onset time were evaluated to determine the feasibility of their application in the development of a real time closed loop seizure intervention program (RCLSIP). The criteria chosen for the performance evaluation were, high statistical robustness as determined through the predictability index, the sensitivity and the specificity of a given measure to detect an EEG seizure, the lag in seizure detection with respect to the EEG seizure onset time, as determined through visual inspection and the computational efficiency for each detection measure. An optimality function was designed to evaluate the overall performance of each measure dependent on the criteria chosen. While each of the above measures analyzed for seizure detection performed very well in terms of the statistical parameters, the nonlinear embedding delay measure was found to have the highest optimality index due to its ability to detect seizure very close to the EEG seizure onset time, thereby making it the most suitable dynamical measure in the development of RCLSIP in rat model with chronic limbic epilepsy.

The Sizing and Optimization Language (SOL): A computer language to improve the user/optimizer interface

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Scotti, S. J.

1989-01-01

The nonlinear mathematical programming method (formal optimization) has had many applications in engineering design. A figure illustrates the use of optimization techniques in the design process. The design process begins with the design problem, such as the classic example of the two-bar truss designed for minimum weight as seen in the leftmost part of the figure. If formal optimization is to be applied, the design problem must be recast in the form of an optimization problem consisting of an objective function, design variables, and constraint function relations. The middle part of the figure shows the two-bar truss design posed as an optimization problem. The total truss weight is the objective function, the tube diameter and truss height are design variables, with stress and Euler buckling considered as constraint function relations. Lastly, the designer develops or obtains analysis software containing a mathematical model of the object being optimized, and then interfaces the analysis routine with existing optimization software such as CONMIN, ADS, or NPSOL. This final state of software development can be both tedious and error-prone. The Sizing and Optimization Language (SOL), a special-purpose computer language whose goal is to make the software implementation phase of optimum design easier and less error-prone, is presented.

Charging power optimization for nonlinear vibration energy harvesting systems subjected to arbitrary, persistent base excitations

NASA Astrophysics Data System (ADS)

Dai, Quanqi; Harne, Ryan L.

2018-01-01

The vibrations of mechanical systems and structures are often a combination of periodic and random motions. Emerging interest to exploit nonlinearities in vibration energy harvesting systems for charging microelectronics may be challenged by such reality due to the potential to transition between favorable and unfavorable dynamic regimes for DC power delivery. Therefore, a need exists to devise an optimization method whereby charging power from nonlinear energy harvesters remains maximized when excitation conditions are neither purely harmonic nor purely random, which have been the attention of past research. This study meets the need by building from an analytical approach that characterizes the dynamic response of nonlinear energy harvesting platforms subjected to combined harmonic and stochastic base accelerations. Here, analytical expressions are formulated and validated to optimize charging power while the influences of the relative proportions of excitation types are concurrently assessed. It is found that about a 2 times deviation in optimal resistive loads can reduce the charging power by 20% when the system is more prominently driven by harmonic base accelerations, whereas a greater proportion of stochastic excitation results in a 11% reduction in power for the same resistance deviation. In addition, the results reveal that when the frequency of a predominantly harmonic excitation deviates by 50% from optimal conditions the charging power reduces by 70%, whereas the same frequency deviation for a more stochastically dominated excitation reduce total DC power by only 20%. These results underscore the need for maximizing direct current power delivery for nonlinear energy harvesting systems in practical operating environments.

Solving Fractional Programming Problems based on Swarm Intelligence

NASA Astrophysics Data System (ADS)

Raouf, Osama Abdel; Hezam, Ibrahim M.

2014-04-01

This paper presents a new approach to solve Fractional Programming Problems (FPPs) based on two different Swarm Intelligence (SI) algorithms. The two algorithms are: Particle Swarm Optimization, and Firefly Algorithm. The two algorithms are tested using several FPP benchmark examples and two selected industrial applications. The test aims to prove the capability of the SI algorithms to solve any type of FPPs. The solution results employing the SI algorithms are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Swarm Intelligence can be denoted as an effective technique for solving linear or nonlinear, non-differentiable fractional objective functions. Problems with an optimal solution at a finite point and an unbounded constraint set, can be solved using the proposed approach. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using the two SI algorithms revealed the superiority of the proposed technique among others in computational time. A better accuracy was remarkably observed in the solution results of the industrial application problems.

Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo

2018-04-01

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.

BEARKIMPE-2: A VBA Excel program for characterizing granular iron in treatability studies

NASA Astrophysics Data System (ADS)

Firdous, R.; Devlin, J. F.

2014-02-01

The selection of a suitable kinetic model to investigate the reaction rate of a contaminant with granular iron (GI) is essential to optimize the permeable reactive barrier (PRB) performance in terms of its reactivity. The newly developed Kinetic Iron Model (KIM) determines the surface rate constant (k) and sorption parameters (Cmax &J) which were not possible to uniquely identify previously. The code was written in Visual Basic (VBA), within Microsoft Excel, was adapted from earlier command line FORTRAN codes, BEARPE and KIMPE. The program is organized with several user interface screens (UserForms) that guide the user step by step through the analysis. BEARKIMPE-2 uses a non-linear optimization algorithm to calculate transport and chemical kinetic parameters. Both reactive and non-reactive sites are considered. A demonstration of the functionality of BEARKIMPE-2, with three nitroaromatic compounds showed that the differences in reaction rates for these compounds could be attributed to differences in their sorption behavior rather than their propensities to accept electrons in the reduction process.

Modern meta-heuristics based on nonlinear physics processes: A review of models and design procedures

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.

2016-10-01

Meta-heuristic algorithms are problem-solving methods which try to find good-enough solutions to very hard optimization problems, at a reasonable computation time, where classical approaches fail, or cannot even been applied. Many existing meta-heuristics approaches are nature-inspired techniques, which work by simulating or modeling different natural processes in a computer. Historically, many of the most successful meta-heuristic approaches have had a biological inspiration, such as evolutionary computation or swarm intelligence paradigms, but in the last few years new approaches based on nonlinear physics processes modeling have been proposed and applied with success. Non-linear physics processes, modeled as optimization algorithms, are able to produce completely new search procedures, with extremely effective exploration capabilities in many cases, which are able to outperform existing optimization approaches. In this paper we review the most important optimization algorithms based on nonlinear physics, how they have been constructed from specific modeling of a real phenomena, and also their novelty in terms of comparison with alternative existing algorithms for optimization. We first review important concepts on optimization problems, search spaces and problems' difficulty. Then, the usefulness of heuristics and meta-heuristics approaches to face hard optimization problems is introduced, and some of the main existing classical versions of these algorithms are reviewed. The mathematical framework of different nonlinear physics processes is then introduced as a preparatory step to review in detail the most important meta-heuristics based on them. A discussion on the novelty of these approaches, their main computational implementation and design issues, and the evaluation of a novel meta-heuristic based on Strange Attractors mutation will be carried out to complete the review of these techniques. We also describe some of the most important application areas, in broad sense, of meta-heuristics, and describe free-accessible software frameworks which can be used to make easier the implementation of these algorithms.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Optimal synthesis and design of the number of cycles in the leaching process for surimi production.

PubMed

Reinheimer, M Agustina; Scenna, Nicolás J; Mussati, Sergio F

2016-12-01

Water consumption required during the leaching stage in the surimi manufacturing process strongly depends on the design and the number and size of stages connected in series for the soluble protein extraction target, and it is considered as the main contributor to the operating costs. Therefore, the optimal synthesis and design of the leaching stage is essential to minimize the total annual cost. In this study, a mathematical optimization model for the optimal design of the leaching operation is presented. Precisely, a detailed Mixed Integer Nonlinear Programming (MINLP) model including operating and geometric constraints was developed based on our previous optimization model (NLP model). Aspects about quality, water consumption and main operating parameters were considered. The minimization of total annual costs, which considered a trade-off between investment and operating costs, led to an optimal solution with lesser number of stages (2 instead of 3 stages) and higher volumes of the leaching tanks comparing with previous results. An analysis was performed in order to investigate how the optimal solution was influenced by the variations of the unitary cost of fresh water, waste treatment and capital investment.

Time optimal control of a jet engine using a quasi-Hermite interpolation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Comiskey, J. G.

1979-01-01

This work made preliminary efforts to generate nonlinear numerical models of a two-spooled turbofan jet engine, and subject these models to a known method of generating global, nonlinear, time optimal control laws. The models were derived numerically, directly from empirical data, as a first step in developing an automatic modelling procedure.

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.

Design of Life Extending Controls Using Nonlinear Parameter Optimization

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Holmes, Michael S.; Ray, Asok

1998-01-01

This report presents the conceptual development of a life extending control system where the objective is to achieve high performance and structural durability of the plant. A life extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel and oxidizer turbines while achieving high performance for transient responses of the combustion chamber pressure and the O2/H2 mixture ratio. This design approach makes use of a combination of linear and nonlinear controller synthesis techniques and also allows adaptation of the life extending controller module to augment a conventional performance controller of a rocket engine. The nonlinear aspect of the design is achieved using nonlinear parameter optimization of a prescribed control structure.

A novel track-before-detect algorithm based on optimal nonlinear filtering for detecting and tracking infrared dim target

NASA Astrophysics Data System (ADS)

Tian, Yuexin; Gao, Kun; Liu, Ying; Han, Lu

2015-08-01

Aiming at the nonlinear and non-Gaussian features of the real infrared scenes, an optimal nonlinear filtering based algorithm for the infrared dim target tracking-before-detecting application is proposed. It uses the nonlinear theory to construct the state and observation models and uses the spectral separation scheme based Wiener chaos expansion method to resolve the stochastic differential equation of the constructed models. In order to improve computation efficiency, the most time-consuming operations independent of observation data are processed on the fore observation stage. The other observation data related rapid computations are implemented subsequently. Simulation results show that the algorithm possesses excellent detection performance and is more suitable for real-time processing.

Bilinear modeling and nonlinear estimation

NASA Technical Reports Server (NTRS)

Dwyer, Thomas A. W., III; Karray, Fakhreddine; Bennett, William H.

1989-01-01

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Parameter Design and Optimal Control of an Open Core Flywheel Energy Storage System

NASA Technical Reports Server (NTRS)

Pang, D.; Anand, D. K.; Kirk, J. A.

1996-01-01

In low earth orbit (LEO) satellite applications spacecraft power is provided by photovoltaic cells and batteries. To overcome battery shortcomings the University of Maryland, working in cooperation with NASA/GSFC and NASA/LeRC, has developed a magnetically suspended flywheel for energy storage applications. The system is referred to as an Open Core Composite Flywheel (OCCF) energy storage system. Successful application of flywheel energy storage requires integration of several technologies, viz. bearings, rotor design, motor/generator, power conditioning, and system control. In this paper we present a parameter design method which has been developed for analyzing the linear SISO model of the magnetic bearing controller for the OCCF. The objective of this continued research is to principally analyze the magnetic bearing system for nonlinear effects in order to increase the region of stability, as determined by high speed and large air gap control. This is achieved by four tasks: (1) physical modeling, design, prototyping, and testing of an improved magnetically suspended flywheel energy storage system, (2) identification of problems that limit performance and their corresponding solutions, (3) development of a design methodology for magnetic bearings, and (4) design of an optimal controller for future high speed applications. Both nonlinear SISO and MIMO models of the magnetic system were built to study limit cycle oscillations and power amplifier saturation phenomenon observed in experiments. The nonlinear models include the inductance of EM coils, the power amplifier saturation, and the physical limitation of the flywheel movement as discussed earlier. The control program EASY5 is used to study the nonlinear SISO and MIMO models. Our results have shown that the characteristics and frequency responses of the magnetic bearing system obtained from modeling are comparable to those obtained experimentally. Although magnetic saturation is shown in the bearings, there are good correlations between the theoretical model and experimental data. Both simulation and experiment confirm large variations of the magnetic bearing characteristics due to air gap growth. Therefore, the gap growth effect should be considered in the magnetic bearing system design. Additionally, the magnetic bearing control system will be compared to other design methods using not only parameter design but H-infinity optimal control and mu synthesis.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.