Yan-Na Jia, Can Jin, Xiu-Fang Yu
Abstract:
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.
Submitted June 14, 2024. Published December 3. 2024.
Math Subject Classifications: 93C20, 35L05.
Key Words: Output tracking; internal model dynamic; error feedback; wave equation.
DOI: 10.58997/ejde.2024.80
Show me the PDF file (721 KB), TEX file for this article.
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Yan-Na Jia School of Mathematics and Statistics Taiyuan Normal University Taiyuan Shanxi 030619, China email: jiayanna1224@126.com |
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Can Jin School of Mathematics and Statistics Taiyuan Normal University Taiyuan Shanxi 030619, China email: jclllnnn@163.com |
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Xiu-Fang Yu School of Mathematics and Statistics Taiyuan Normal University Taiyuan Shanxi 030619, China email: yuxiufang@tyut.edu.cn |
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