Parameter estimation and velocity signal extraction for one-dimensional wave equation with harmonic corrupted boundary observation

Abstract In this paper, we consider parameter estimation and velocity signal extraction from a disturbed boundary velocity signal for an unstable wave equation. Firstly, an adaptive observer is designed based on the boundary displacement and the corrupted boundary velocity. Then the design of the fe...

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Bibliographic Details
Published in:IMA journal of mathematical control and information 2023-06, Vol.40 (2), p.385-402
Main Authors: Huang, Shuangxi, Jin, Feng-Fei
Format: Article
Language:English
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Summary:Abstract In this paper, we consider parameter estimation and velocity signal extraction from a disturbed boundary velocity signal for an unstable wave equation. Firstly, an adaptive observer is designed based on the boundary displacement and the corrupted boundary velocity. Then the design of the feedback law adopts the backstepping method of infinite dimensional system. Finally, as time approaches infinity, the estimated parameters converge to the unknown parameters, the initial value disturbance can be obtained, and the velocity signal can be asymptotically recovered. Meanwhile, the asymptotic stability of the closed-loop system can be proved by $C_{0}$-semigroup theory and Lyapunov method. Numerical simulation shows that the proposed scheme is reasonable.
ISSN:0265-0754
1471-6887
DOI:10.1093/imamci/dnad018