A parameter optimization approach to solving quasi-LMI problems

Author

Zheng, Feng ; Wang, Qing-Guo ; Lee, Tong Heng

Author_Institution

Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore

Volume

4

fYear

2001

fDate

2001

Firstpage

3607

Abstract

Many canonical and modern control problems can be recast into the problem of solving a group of matrix inequalities. Some of them are in the form of linear matrix inequalities (LMIs), which can be solved very efficiently by the powerful LMI toolbox in Matlab, but some others are in the form of quasi LMIs (QLMIs). By quasi, we mean that unknown parameters are involved in the matrix inequalities and these inequalities are LMIs only when the unknown parameters are fixed. Thus how to "guess" the unknown parameters is the key to solve the whole problem. In this paper, we present an optimal estimate for the unknown parameters. We will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems. Numerical examples are provided to show the effectiveness of the proposed method

Keywords

feedback; matrix algebra; optimal control; optimisation; linear matrix inequalities; optimal estimate; overshoot bound control; parameter optimization approach; quasi-LMI problems; reachable set analysis; Adaptive control; Closed loop systems; Control system synthesis; Control systems; Ear; Eigenvalues and eigenfunctions; Linear matrix inequalities; Uncertain systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980420

Filename

980420