An approximation theory for strongly stabilizing solutions to the operator LQ Riccati equation

Author

Oostveen, J.C. ; Curtain, R.F. ; Ito, K.

Author_Institution

Dept. of Math. & Comput. Sci., Groningen Univ., Netherlands

Volume

1

fYear

2001

fDate

2001

Firstpage

123

Abstract

The linear-quadratic (LQ) control problem is considered for a class of infinite-dimensional systems with bounded input and output operators, that are not exponentially stabilizable, but only strongly stabilizable. A sufficient condition for the existence of a minimizing control and of a stabilizing solution to the associated LQ Riccati equation is given. The main contribution of the paper is the convergence of the stabilizing solutions of a sequence of finite-dimensional Riccati equations to the strongly stabilizing solution of the infinite-dimensional Riccati equation. We illustrate the approximation result with an example of LQ control for a model of propagation of sound waves in a one-dimensional waveguide

Keywords

Hilbert spaces; Riccati equations; control system synthesis; convergence; group theory; linear quadratic control; multidimensional systems; stability; approximation theory; bounded input operators; bounded output operators; finite-dimensional Riccati equations; infinite-dimensional systems; linear-quadratic control; one-dimensional waveguide; operator LQ Riccati equation; sound waves; strongly stabilizable systems; strongly stabilizing solutions; Acoustic propagation; Actuators; Approximation methods; Computer science; Control systems; Hilbert space; Mathematical model; Mathematics; Riccati equations; Sufficient conditions;

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/.2001.980083

Filename

980083