An adaptive controller for infinite dimensional dynamical systems

Author

Demetriou, M.A. ; Ito, K.

Author_Institution

Dept. of Math., North Carolina State Univ., Raleigh, NC, USA

Volume

3

fYear

1995

fDate

13-15 Dec 1995

Firstpage

2940

Abstract

An adaptive controller for a perturbed infinite dimensional plant is developed to force the state of the plant track the state of a reference model. The reference model is based on the nominal plant and has a physical similarity with the plant. Using a Lyapunov stability argument, which is based on the H^∞-Riccati equation of the nominal plant, an adaptive law is developed for the adjustment of the feedback gain. It is proved that the closed-loop system is stable with the tracking error remaining bounded, and converging to zero provided that the norm of the structured perturbation is less than a specified attenuation bound. Numerical simulation of a heat equation is presented to demonstrate the applicability of the proposed adaptive scheme

Keywords

H^∞ control; Hilbert spaces; Lyapunov methods; Riccati equations; closed loop systems; feedback; model reference adaptive control systems; multidimensional systems; H^∞-Riccati equation; Lyapunov stability argument; adaptive controller; closed-loop system; feedback gain; heat equation; infinite dimensional dynamical systems; numerical simulation; perturbed infinite dimensional plant; tracking error; Adaptive control; Adaptive systems; Attenuation; Control system synthesis; Control systems; Equations; Feedback; Force control; Lyapunov method; Programmable control;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.478590

Filename

478590