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IMA Journal of Mathematical Control and Information Advance Access originally published online on October 30, 2009
IMA Journal of Mathematical Control and Information 2009 26(4):395-415; doi:10.1093/imamci/dnp020
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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.

An adaptive tracking controller design for non-linear singularly perturbed systems using fuzzy singularly perturbed model

Li Li{dagger}

College of Computer and Information Engineering, Tianjin Normal University, Tianjin 300387, People's Republic of China

F. C. Sun

Department of Computer Science and Technology, State Key Lab of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, People's Republic of China

{dagger} Email: ll-03{at}mails.tsinghua.edu.cn

Received on October 26, 2008; Revision received May 10, 2009. Accepted on July 12, 2009

For a class of non-linear singularly perturbed systems with unknown dynamic and external disturbance, an adaptive tracking controller using fuzzy singularly perturbed model is developed. First, a series of dynamic Takagi-Sugeno fuzzy singularly perturbed subsystems are built to approximate a non-linear singularly perturbed system and a stable reference model with the same fuzzy premise is chosen to design both expected trajectory and dynamic performance. Then, a kind of controller including adaptive feedback term is developed to make the states of the closed-loop system follow those of the reference model. The linear feedback gain of the controller can be solved by the linear matrix inequality approach. The adaptive sliding term is used to compensate the uncertainty and alleviate the disturbance. Lyapunov constitute techniques can be used to prove the stability of the closed-loop systems. Finally, the simulations results illustrate the effectiveness of this approach.

Keywords: adaptive control; LMI; TS fuzzy logic system; non-linear singularly perturbed system.


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