Application of variational iteration method for Hamilton-Jacobi-Bellman equations

被引：36
作者：
Kafash, B. [1 ]
Delavarkhalafi, A. [1 ]
Karbassi, S. M. [2 ]
机构：
[1] Yazd Univ, Fac Math, Yazd, Iran
[2] Islamic Azad Univ, Fac Adv Educ, Yazd Branch, Yazd, Iran
来源：
APPLIED MATHEMATICAL MODELLING | 2013年 / 37卷 / 06期
关键词：
Optimal control problems; Hamilton-Jacobi-Bellman (HJB) Equations; Variational iteration method (VIM); Banach's fixed point theorem; APPROXIMATE-ANALYTICAL SOLUTION; CONVERGENCE;
D O I：
10.1016/j.apm.2012.08.013
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we use the variational iteration method (VIM) for optimal control problems. First, optimal control problems are transferred to Hamilton-Jacobi-Bellman (HJB) equation as a nonlinear first order hyperbolic partial differential equation. Then, the basic VIM is applied to construct a nonlinear optimal feedback control law. By this method, the control and state variables can be approximated as a function of time. Also, the numerical value of the performance index is obtained readily. In view of the convergence of the method, some illustrative examples are presented to show the efficiency and reliability of the presented method. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：3917 / 3928
页数：12
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