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IMA Journal of Mathematical Control and Information Advance Access originally published online on April 28, 2009
IMA Journal of Mathematical Control and Information 2009 26(2):179-196; doi:10.1093/imamci/dnp007
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Adaptive stabilization of a sine-Gordon equation with input disturbances

Toshihiro Kobayashi{dagger}

Department of Mechanical and Control Engineering, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan

{dagger} Email: koba{at}cntl.kyutech.ac.jp

Received on October 5, 2008; Revision received January 6, 2009. Accepted on March 17, 2009

This paper is concerned with adaptive stabilization of the system governed by the sine-Gordon equation with input disturbances. The adaptive boundary controller is constructed by the concept of high-gain adaptive feedback and the estimation mechanism for the unknown parameters of the disturbances. The well posedness of the closed-loop system is justified. After the boundedness of the solution is shown, the stability of the closed-loop system and the convergence of the system state to zero are guaranteed by the LaSalle's invariance principle. The system with output disturbances is also discussed.

Keywords: sine-Gordon equation; adaptive stabilization; boundary control; non-linear observability.


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