Adaptive output tracking for 1-D wave equations subject to unknown harmonic disturbances

In this paper, we are concerned with an adaptive output tracking problem for one-dimensional anti-stable wave equations with unknown harmonic disturbance and reference signals which have both unknown frequencies and amplitudes. The output and disturbance are non-collocated to the control input. Firs...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 69; no. 4; pp. 1 - 8
Main Authors Wu, Xiao-Hui, Wang, Jun-Min
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Adaptation models
adaptive
anti-stable wave equation
Backstepping
Error analysis
error feedback
Harmonic analysis
Mathematical models
Numerical simulation
output tracking
Propagation
Reference signals
Tracking errors
Tracking problem
Trajectory
unknown harmonic disturbances
Wave equations
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Summary:In this paper, we are concerned with an adaptive output tracking problem for one-dimensional anti-stable wave equations with unknown harmonic disturbance and reference signals which have both unknown frequencies and amplitudes. The output and disturbance are non-collocated to the control input. First, we construct an auxiliary system and internal model dynamic to restructure the measurable tracking error such that the error consists of these available states. Then, an adaptive method is used to estimate the unknown parameters. Using an invertible transformation, we convert the non-collocated configuration into the collocated ones so that the conventional method can be applied. Finally, error-based feedback is proposed to realize output tracking. Numerical simulations validate these theoretical results.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3333797