Stability region estimates for SDRE controlled systems using sum of squares optimization

Author

Seiler, Pete

Author_Institution

Dept. of Mech. & Ind. Eng., Illinois Univ., Urbana, IL, USA

Volume

3

fYear

2003

fDate

4-6 June 2003

Firstpage

1867

Abstract

In this paper, we investigate the state-dependent Riccati equation (SDRE) method to control nonlinear systems. This method stabilizes the closed loop system around the origin. However, the global asymptotic stability is not ensured. Moreover, the stability analysis is complicated because the closed loop system is typically not known in a closed form. We present a theorem that turns stability region estimation into a functional search problem. Results on the sum of squares polynomials are used to turn this search into a semi-definite programming problem. A simple example demonstrating this method is given.

Keywords

Riccati equations; asymptotic stability; closed loop systems; mathematical programming; nonlinear systems; optimisation; asymptotic stability; closed loop system; functional search; nonlinear systems; semidefinite programming; stability region estimation; state dependent Riccati equation control system; sum of squares optimization; sum of squares polynomials; Asymptotic stability; Closed loop systems; Control systems; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Polynomials; Riccati equations; Search problems; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1243345

Filename

1243345