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Stabilization and regulator design for a one‐dimensional unstable wave equation with input harmonic disturbance
Author(s) -
Guo Wei,
Guo BaoZhu
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1843
Subject(s) - backstepping , control theory (sociology) , disturbance (geology) , regulator , harmonic , instability , mathematics , stability (learning theory) , adaptive control , computer science , control (management) , physics , mechanics , geology , paleontology , biochemistry , chemistry , quantum mechanics , artificial intelligence , machine learning , gene
SUMMARY This paper considers the parameter estimation and stabilization of a one‐dimensional wave equation with instability suffered at one end and uncertainty of harmonic disturbance at the controlled end. The backstepping method for infinite‐dimensional system is adopted in the design of the adaptive regulator. It is shown that the resulting closed‐loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity. Copyright © 2011 John Wiley & Sons, Ltd.