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Adaptive stabilization of coupled PDE–ODE systems with multiple uncertainties∗

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.cn School 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
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Abstract

The adaptive stabilization is investigated for a class of coupled PDE-ODE systems with multiple uncertainties. The presence of the multiple uncertainties and the interaction between the sub-systems makes the systems to be considered more general and representative, and moreover it may result in the ineffectiveness of the conventional methods on this topic. Motivated by the existing literature, an infinite-dimensional backsteppping transformation with new kernel functions is first introduced to change the original system into a target system, from which the control design and performance analysis of the original system will become quite convenient. Then, by certainty equivalence principle and Lyapunov method, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. A simulation example is provided to validate the proposed method.

Keywords

Coupled PDE-ODE systemsspatially varying coefficientadaptive stabilizationinfinite-dimensional backstepping
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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