Output tracking for a 1-D wave equations with spatially varying coefficients and subject to unknown disturbances

In this article, we study the output tracking problem for a wave  equation with variable coefficients, and subject to boundary control  matched disturbances. Both the disturbances and the reference signal are  unknown harmonic signal. The performance output is non-collocated with  the control input....

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2024; no. 1-??; pp. 80 - 14
Main Authors Jia, Yan-Na, Jin, Can, Yu, Xiu-Fang
Format Journal Article
LanguageEnglish
Published Texas State University 03.12.2024
Subjects
error feedback
internal model dynamic
output tracking
wave equation
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ISSN1072-6691
1072-6691
DOI10.58997/ejde.2024.80

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Summary:In this article, we study the output tracking problem for a wave  equation with variable coefficients, and subject to boundary control  matched disturbances. Both the disturbances and the reference signal are  unknown harmonic signal. The performance output is non-collocated with  the control input. Initially, we establish an undisturbed auxiliary system  and devise an appropriate internal model dynamic to reformulate the  tracking error. Subsequently, we introduce an error-based feedback  controller, leveraging an invertible transformation to achieve output  tracking. The well-posedness and stability of the closed-loop system are  established by applying semigroup theory approach. Finally, we illustrate  the effectiveness of these theoretical results with numerical simulations. For more information see https://ejde.math.txstate.edu/Volumes/2024/80/abstr.html  
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2024.80