An Iterative Method for Optimal Feedback Control and Generalized HJB Equation  

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

机构地区：[1]the school of applied mathematics,guangdong university of technology,Guangzhou 510006,China [2]the school of electromechanical engineering,guangdong university of technology,Guangzhou 510006,China

出　　处：《IEEE/CAA Journal of Automatica Sinica》2018年第5期999-1006,共8页自动化学报（英文版）

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)

摘　　要：Abstract--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. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.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.

关 键 词：Generalized Hamilton-Jacobi-Bellman(HJB) equation iterative method nonlinear dynamic system optimal control 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]