A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

We introduce a numerical method to solve stochastic optimal control problems which are linear in the control. We facilitate the idea of solving two-point boundary value problems with spline functions in order to solve the resulting dynamic programming equation. We then show how to effectively reduce the dimension in the proposed algorithm, which improves computational time and memory constraints. An example, motivated as an invest problem with uncertain cost, is provided, and the effectiveness of our method demonstrated.     

Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method

This research focuses on pre-disaster transportation network protection against uncertain future disasters. Given limited resources, the goal of the central planner is to choose the best set of network components to protect while allowing the network users to follow their own best-perceived routes in any resultant network configuration. This problem is formulated as a two-stage stochastic programming problem with equilibrium constraints, where the objective is to minimize the total expected physical and social losses caused by potential disasters. Developing efficient solution methods for such a problem can be challenging. In this work, we will demonstrate the applicability of progressive hedging-based method for solving large scale stochastic network optimization problems with equilibrium constraints. In the proposed solution procedure, we solve each modified scenario sub-problem as a mathematical program with complementary constraints and then gradually aggregate scenario-dependent solutions to the final optimal solution.     

Solving Optimal Control Problems on the Class of Step Functions

Linear optimal control problems with multipoint non-separated conditions with a quadratic performance criterion of control are analyzed. An approach with a violation of intermediate conditions is proposed. The original problem is reduced to the classical quadratic programming problem with the dimension determined by the number of intermediate points. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 153–162, July–August 2005.     

Optimal Control of Nonlinear Stochastic Systems under Constraints: An Approximate Determination Method

An approximate method is developed for determining the optimal control for nonlinear stochastic systems under mixed equality- and inequality-type constraints on the parameters of the system, control functions, and phase coordinate in the presence of random parameters and additive and multiplicative noises. The method is based on the reduction of the initial stochastic problem to a deterministic problem for the cumulants of a random process described by stochastic differential equations.     

Optimal Control and Stochastic Simulation of Large Nonlinear Models with Rational Expectations

This paper presents a computationally fesible procedure for the optimalcontrol and stochastic simulation of large nonlinear models with rationalexpectations under the assumption of certainty equivalence.     

Lipschitzian Regularity of the Minimizing Trajectories for Nonlinear Optimal Control Problems

We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions can we assure optimal controls are bounded? This question is related to one of Lipschitzian regularity of optimal trajectories, and the answer to it is crucial in closing the gap between the conditions arising in existence theory and necessary optimality conditions. Rewriting the Lagrange problem in a parametric form, we obtain a relation between the applicability conditions of the Pontryagin maximum principle to the latter problem and the Lipschitzian regularity conditions for the original problem. Under the standard hypotheses of coercivity of the existence theory, the conditions imply that the optimal controls are essentially bounded, assuring the applicability of the classical necessary optimality conditions like the Pontryagin maximum principle. The result extends previous Lipschitzian regularity results to cover optimal control problems with general nonlinear dynamics.     

Finite Horizon Minimax Optimal Control of Nonlinear Continuous Time Systems with Stochastic Uncertainty

This paper develops a general continuous-time stochastic framework for robustness analysis and robust control synthesis. We consider a stochastic minimax optimization problem for general stochastic uncertain systems. A general method is presented for converting problems of performance analysis or controller synthesis into unconstrained optimization problems.     

Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing

Hubs are special facilities designed to act as switching, transshipment and sorting points in various distribution systems. Since hub facilities concentrate and consolidate flows, disruptions at hubs could have large effects on the performance of a hub network. In this paper, we have formulated the multiple allocation p-hub median problem under intentional disruptions as a bi-level game model. In this model, the follower’s objective is to identify those hubs the loss of which would most diminish service efficiency. Moreover, the leader’s objective is to identify the set of hubs to locate in order to minimize expected transportation cost while taking normal and failure conditions into account. We have applied two algorithms based on simulated annealing to solve the defined problem. In addition, the algorithms have been calibrated using the Taguchi method. Computational experiments on different instances indicate that the proposed algorithms would be efficient in practice.     

解一类最优控制问题的一种自适应拟谱方法

提出一种解常微分方程最优控制问题的自适应拟谱方法.对状态函数和控制函数使用不同次数的多项式逼近.设计了一个自适应算法决定不同的次数,并给出了理论分析.数值算例比较了本文方法与一种常用的拟谱方法.     

Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach

In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are proposed. An NN is used to approximate the time-varying cost function using the method of least squares on a predefined region. The result is an NN nearly -constrained feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated in two examples, including a nonholonomic system.     

Effect of Displacement of Optimal Control in Stabilization Problems for Quasi-Linear Diffusion-Type Stochastic Systems

Journal of Computer and Systems Sciences International - A displacement effect of a linear optimal control in stabilization problems for diffusion-type stochastic systems that operate on an...     

The Use of Legendre Polynomial Expansions in Solving Optimal Control Problems in the Space l 2

A method for solving a class of general deterministic optimal control problems is presented here. The method consists of relating the functions involved in the problem to sequences and then converting the problem to one which deals with these sequences alone. The function-sequence correspondence is defined by representing each function by its Legendre polynomial expansion and then relating the function to the sequence of coefficients in this expansion. After this is done, the problem is converted to one in l ²; by determining the equivalents in l ²; of differentiation, inner multiplication, and multiplication.

The resulting problem in l ²; is a non-linear programming problem which consists of an infinite array of equations, inequalities, and expressions, each of which involves infinite polynomial expressions. To solve a problem of this type it must be approximated by a finite non-linear programming problem. After this is done various methods can bo used for solving the final problem.     

利用串行最小优化算法求解回归估计问题

支撑矢量机是以Vapnik的统计学习理论为基础,以结构风险最小化为原则的新型学习机。目前,对它的研究是国际上的一个研究热点。针对大数据量的回归估计问题,论文提出了一种新的求解方法。为了说明该方法的有效性,给出了数值模拟的例子。     

A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems

A new Chebyshev finite difference method for solving class of optimal control problem is proposed. The algorithm is based on Chebyshev approximations of the derivatives arising in system dynamics. In the performance index, we use Chebyshev approximations for integration. The numerical examples illustrate the robustness, accuracy and efficiency of the proposed technique.     

网络控制系统的随机最优控制综述

网络控制系统由于网络的引入而出现了数据延迟。在处理随机发生的延迟上,用最优控制的方法是比较有效的。目前为止出现了不少有关网络控制系统的最优控制的结果,论文旨在对网络控制系统的最优控制方面的研究现状进行介绍,并指出进一步研究的方向。     

Parallel Optimal Control for Weakly Coupled Nonlinear Systems Using Successive Galerkin Approximation

This technical note presents a new algorithm for the closed-loop parallel optimal control of weakly coupled nonlinear systems with respect to performance criteria using the successive Galerkin approximation (SGA). By using the weak coupling theory, the optimal control law can be obtained from two reduced-order optimal control problems in parallel, but the resulting problem is difficult to solve for nonlinear systems. In order to overcome the difficulties inherent in the nonlinear optimal control problem, the parallel optimal control laws are constructed in terms of the approximated solutions to two independent Hamilton-Jacobi-Bellman equations using the SGA method. One of the purposes of this note is to design the closed-loop parallel optimal control law for the weakly coupled nonlinear systems using the SGA method. The second is to reduce the computational complexity when the SGA method is applied to the high-order weakly coupled systems.      

Nonlinear Stochastic Systems under Constraints: Optimization of Their Control

Conditions of controllability and control optimality for nonlinear dynamic systems under the action of random parameters, multiplicative and additive noises, and mixed equality- and inequality-type constraints on the parameters of the system, control functions, and state vector of phase coordinates are determined within the framework of the theory of Markov diffusion processes.     

在Windows下使用五笔字型输入法常见问题及解决方法

讨论了98王码WB9801五笔字型输入法软件在Windows环境下使用时应注意的问题、出现异常现象的解决方法及使用技巧。