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IMA Journal of Mathematical Control and Information Advance Access originally published online on September 5, 2007
IMA Journal of Mathematical Control and Information 2008 25(2):205-219; doi:10.1093/imamci/dnm019
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Adaptive regulator design for undamped second-order hyperbolic systems with output disturbances

Toshihiro Kobayashi{dagger}, Tetsuzo Sakamoto{ddagger} and Masahiro Oya§

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

{ddagger} Email: sakamoto{at}cntl.kyutech.ac.jp

§ Email: oya{at}cntl.kyutech.ac.jp

Received on June 28, 2006; Revision received March 15, 2007. Accepted on April 10, 2007

In this paper, an adaptive regulator is designed for undamped second-order hyperbolic systems with output disturbances in the case where the input and output operators are collocated. The systems may have an infinite number of poles and zeros on the imaginary axis. The adaptive regulator is constructed by a high-gain adaptive feedback and a new type of the estimation mechanism for the unknown parameters of the disturbances. First, the well-posedness of the closed-loop system is justified. Next, the stability of the closed-loop system is analysed. An example is given to illustrate the theory.

Keywords: high-gain adaptive stabilization; regulator design; undamped second-order hyperbolic systems; disturbed outputs.


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