An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

作     者：Xuesong Chen Xin Chen Xuesong Chen;Xin Chen

作者机构：the school of applied mathematicsguangdong university of technologyGuangzhou 510006China the school of electromechanical engineeringguangdong university of technologyGuangzhou 510006China 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报（英文版）)

年 卷 期：2018年第5卷第5期

页      面：999-1006页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 08[工学] 0802[工学-机械工程] 0811[工学-控制科学与工程] 080201[工学-机械制造及其自动化] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(U1601202,U1134004,91648108) the Natural Science Foundation of Guangdong Province(2015A030313497,2015A030312008) the Project of Science and Technology of Guangdong Province(2015B010102014,2015B010124001,2015B010104006,2018A030313505) 

主　　题：磁悬浮系统 悬浮物 自动控制 自动化系统 

摘      要：In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman(GHJB) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm,which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.