Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem

作     者：Xue-song CHEN 

作者机构：School of Applied MathematicsGuangdong University of TechnologyGuangzhou 510006China 

出 版 物：《Frontiers of Information Technology & Electronic Engineering》 (信息与电子工程前沿（英文版）)

年 卷 期：2017年第18卷第10期

页      面：1479-1487页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 0839[工学-网络空间安全] 070105[理学-运筹学与控制论] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the China Postdoctoral Science Foundation(No.2013M531842) the Natural Science Foundation of Guangdong Province,China(No.2015A030313497) the Science and Technology Program of Guangzhou,China(No.2014KP000039) 

主　　题：Generalized Hamilton-Jacobi-Bellman equation Nonlinear optimal control Galerkin approximation Legendre polynomials 

摘      要：We investigate the use of an approximation method for obtaining near-optimal solutions to a kind of nonlinear continuous-time(CT) system. The approach derived from the Galerkin approximation is used to solve the generalized Hamilton-Jacobi-Bellman(GHJB) equations. The Galerkin approximation with Legendre polynomials(GALP) for GHJB equations has not been applied to nonlinear CT systems. The proposed GALP method solves the GHJB equations in CT systems on some well-defined region of attraction. The integrals that need to be computed are much fewer due to the orthogonal properties of Legendre polynomials, which is a significant advantage of this approach. The stabilization and convergence properties with regard to the iterative variable have been proved.Numerical examples show that the update control laws converge to the optimal control for nonlinear CT systems.