Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non‐collocated control |
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| Authors: | Wei Guo Bao‐Zhu Guo Zhi‐Chao Shao |
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| Affiliation: | 1. School of Information Technology and Management, University of International Business and Economics, Beijing 100029, People's Republic of China;2. Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, People's Republic of China;3. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, People's Republic of China;4. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa |
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| Abstract: | This paper is concerned with the parameter estimation and stabilization of a one‐dimensional wave equation with harmonic disturbance suffered by boundary observation at one end and the non‐collocated control at the other end. An adaptive observer is designed in terms of measured velocity corrupted by harmonic disturbance with unknown magnitude. The backstepping method for infinite‐dimensional system is adopted in the design of the feedback law. 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 © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | vibrating string harmonic disturbance rejection boundary control backstepping |
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