Adaptive output regulation for wave PDEs with a nonlocal term and unknown harmonic disturbances

In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave equation with velocity recirculation and unknown harmonic disturbances. The disturbances are present in all channels, and both the disturbances...

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Bibliographic Details
Published inSystems & control letters Vol. 197; p. 106043
Main Authors Liu, Jun-Jun, Peng, Ning, Wang, Jun-Min
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2025
Subjects
Adaptive output tracking
Error feedback
Internal model dynamic
Wave equation
Error feedback
Wave equation
Adaptive output tracking
Internal model dynamic
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Summary:In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave equation with velocity recirculation and unknown harmonic disturbances. The disturbances are present in all channels, and both the disturbances and the reference trajectory have an unknown sinusoidal form. We first construct an auxiliary system and a proper trajectory such that total disturbances appear only in the output of the auxiliary. As a result, we obtain a dynamic estimation of the total disturbances by constructing an internal model dynamics. An adaptive method is proposed to determine the uncertain parameters. In order to realize exponential output tracking, the proposed error-based adaptive dynamic compensator is employed. Finally, some simulation examples are carried out to validate the results.
ISSN:0167-6911
DOI:10.1016/j.sysconle.2025.106043