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Adaptive Output Regulation for an Unstable Wave Equation.

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Bibliographische Detailangaben
Titel:	Adaptive Output Regulation for an Unstable Wave Equation.
Autoren:	Li, Bing‐Sen^1,2 (AUTHOR), Zhou, Hua‐Cheng¹ (AUTHOR) hczhou@amss.ac.cn
Quelle:	International Journal of Adaptive Control & Signal Processing. Dec2025, Vol. 39 Issue 12, p2584-2595. 12p.
Schlagwörter:	ADAPTIVE control systems, BACKSTEPPING control method, FEEDBACK control systems, OBSERVABILITY (Control theory), NONLINEAR wave equations, PERTURBATION theory, *MATHEMATICAL transformations
Abstract:	In this work, we investigate the error feedback regulator problem for an unstable wave equation in which the output is anti‐collocated with the control input, and all feasible channels have disturbance. Through the implementation of a variable transformation, an auxiliary system is derived where the measured error serves as its boundary output, and all unknown disturbances are positioned at the output terminal. Afterward, an adaptive observer is developed to estimate the state of the auxiliary system, as well as the unknown amplitudes of the disturbance and reference signals, depending on the tracking error. We construct an auxiliary system for this observer, wherein all disturbance estimation terms are consolidated at the end alongside the control. By the backstepping method, the final regulator is obtained which is proved to be applicable. Numerical results are shown for the main results. [ABSTRACT FROM AUTHOR]
Datenbank:	Academic Search Index

Beschreibung
Abstract:	In this work, we investigate the error feedback regulator problem for an unstable wave equation in which the output is anti‐collocated with the control input, and all feasible channels have disturbance. Through the implementation of a variable transformation, an auxiliary system is derived where the measured error serves as its boundary output, and all unknown disturbances are positioned at the output terminal. Afterward, an adaptive observer is developed to estimate the state of the auxiliary system, as well as the unknown amplitudes of the disturbance and reference signals, depending on the tracking error. We construct an auxiliary system for this observer, wherein all disturbance estimation terms are consolidated at the end alongside the control. By the backstepping method, the final regulator is obtained which is proved to be applicable. Numerical results are shown for the main results. [ABSTRACT FROM AUTHOR]
ISSN:	08906327
DOI:	10.1002/acs.4071