Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation

被引：519

作者：

Beard, RW ^{[1
]}

Saridis, GN

Wen, JT

机构：

[1] Brigham Young Univ, Dept Elect & Comp Engn, Provo, UT 84602 USA

[2] Rensselaer Polytech Inst, Dept Elect Comp & Syst Engn, Troy, NY 12180 USA

来源：

AUTOMATICA | 1997年 / 33卷 / 12期

关键词：

nonlinear control; optimal control; Galerkin approximation; feedback synthesis; generalized Hamilton-Jacobi-Bellman equation;

D O I：

10.1016/S0005-1098(97)00128-3

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we study the convergence of the Galerkin approximation method applied to the generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman equation. We state sufficient conditions that guarantee that the Galerkin approximation converges to the solution of the GHJB equation and that the resulting approximate control is stabilizing on the same region as the initial control. The method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the LQR design method. (C) 1997 Elsevier Science Ltd. All rights reserved.

引用

页码：2159 / 2177

页数：19

共 71 条

[1] STABILIZATION OF A CLASS OF NONLINEAR-SYSTEMS BY A SMOOTH FEEDBACK-CONTROL [J].

AEYELS, D .

SYSTEMS & CONTROL LETTERS, 1985, 5 (05) :289-294

[2]

Aeyels D., 1986, Theory and Applications of Nonlinear Control Systems, P93

[3] THE SUCCESSIVE APPROXIMATION PROCEDURE FOR FINITE-TIME OPTIMAL-CONTROL OF BILINEAR-SYSTEMS [J].

AGANOVIC, Z ;

GAJIC, Z .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1994, 39 (09) :1932-1935

[4]

ALBREKHT EG, 1961, PMM-J APPL MATH MEC, V25, P836

[5]

Anderson BD, 1971, LINEAR OPTIMAL CONTR, V197

[6]

Apostol TM., 1974, Mathematical Analysis

[7] Global output regulation and disturbance attenuation with global stability via measurement feedback for a class of nonlinear systems [J].

Battilotti, S .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (03) :315-327

[8] FEEDBACK-CONTROL OF NONLINEAR-SYSTEMS BY EXTENDED LINEARIZATION [J].

BAUMANN, WT ;

RUGH, WJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1986, 31 (01) :40-46

[9] Improving the performance of stabilizing controls for nonlinear systems [J].

Bear, R ;

Saridis, G ;

Wen, J .

IEEE CONTROL SYSTEMS MAGAZINE, 1996, 16 (05) :27-35

[10]

BEARD R, 1998, IN PRESS J OPTIM THE

← 1 2 3 4 5 6 7 8 →