Nonlinear optimal control: alternatives to Hamilton-Jacobi equation

Author

Huang, Yun ; Lu, Wei-Min

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

Volume

4

fYear

1996

fDate

11-13 Dec 1996

Firstpage

3942

Abstract

The methods of frozen Riccati equations and nonlinear matrix inequalities (NLMIs) offer certain computational advantages over Hamilton-Jacobi equations (HJE), but may fail to be optimal. The frozen Riccati method uses a non-unique state-dependent linear representation to reduce the HJE to a state-dependent Riccati equation. While there usually exists some choices that recover the optimality, it may be difficult to find. The NLMI computation for analysis and synthesis is shown to be as hard as Lyapunov stability analysis; a finite difference approximation scheme is proposed to solve the NLMIs

Keywords

Riccati equations; approximation theory; control system analysis; matrix algebra; nonlinear control systems; optimal control; Hamilton-Jacobi equations; finite difference approximation; frozen Riccati equations; nonlinear matrix inequality; nonlinear systems; optimal control; Control systems; Ear; Jacobian matrices; Linear matrix inequalities; Lyapunov method; Nonlinear equations; Nonlinear systems; Optimal control; Performance analysis; Riccati equations;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1996., Proceedings of the 35th IEEE Conference on

Conference_Location

Kobe

ISSN

0191-2216

Print_ISBN

0-7803-3590-2

Type

conf

DOI

10.1109/CDC.1996.577297

Filename

577297