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Stabilization and regulator design for a one-dimensional unstable wave equation with input harmonic disturbance

Authors

  • Wei Guo,

    Corresponding author
    • School of Information Technology and Management, University of International Business and Economics, Beijing, China
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  • Bao-Zhu Guo

    1. Academy of Mathematics and System Sciences, Academia Sinica, Beijing, China
    2. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits, Johannesburg, South Africa
    3. School of Mathematical Sciences, Shanxi University, Taiyuan, China
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Correspondence to: Wei Guo, School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China.

E-mail: guowei74@126.com

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.

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