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Adaptive stabilization of coupled PDE–ODE systems with multipleuncertainties∗

Published online by Cambridge University Press:  14 March 2014

Jian Li and
Yungang Liu
Jian Li
Affiliation:
School of Control Science and Engineering, Shandong University, Jinan 250061, P.R. China. lygfr@sdu.edu.cnSchool of Mathematics and Information Science, Yantai University, Yantai 264005, P.R. China
Yungang Liu
Affiliation:
School of Control Science and Engineering, Shandong University, Jinan 250061, P.R. China. lygfr@sdu.edu.cn

Abstract

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The adaptive stabilization is investigated for a class of coupled PDE-ODE systems withmultiple uncertainties. The presence of the multiple uncertainties and the interactionbetween the sub-systems makes the systems to be considered more general andrepresentative, and moreover it may result in the ineffectiveness of the conventionalmethods on this topic. Motivated by the existing literature, an infinite-dimensionalbacksteppping transformation with new kernel functions is first introduced to change theoriginal system into a target system, from which the control design and performanceanalysis of the original system will become quite convenient. Then, by certaintyequivalence principle and Lyapunov method, an adaptive stabilizing controller issuccessfully constructed, which guarantees that all the closed-loop system states arebounded while the original system states converging to zero. A simulation example isprovided to validate the proposed method.

Keywords

Coupled PDE-ODE systemsspatially varying coefficientadaptive stabilizationinfinite-dimensional backstepping

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014, pp. 488 - 516
Copyright
© EDP Sciences, SMAI, 2014

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