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Backstepping approach to the adaptive regulator design for a one-dimensional wave equation with general input harmonic disturbance

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Abstract

This paper considers the parameter estimation and stabilization of an unstable one-dimensional wave equation with matched general 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.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Statistics, University of International Business and Economics, Beijing, 100029, China

    Wei Guo & Zhi-Chao Shao

Authors
  1. Wei Guo
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  2. Zhi-Chao Shao
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Corresponding author

Correspondence to Wei Guo.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant No. 61374088 and the Fundamental Research Funds for the Central Universities in UIBE (15JQ01).

This paper was recommended for publication by Editor CHEN Jie.

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Guo, W., Shao, ZC. Backstepping approach to the adaptive regulator design for a one-dimensional wave equation with general input harmonic disturbance. J Syst Sci Complex 30, 253–279 (2017). https://doi.org/10.1007/s11424-016-5038-z

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  • DOI: https://doi.org/10.1007/s11424-016-5038-z

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