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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 192387, 6 pages
http://dx.doi.org/10.1155/2014/192387
Research Article

Fuzzy Adaptive Prescribed Performance Control for MIMO Uncertain Chaotic Systems in Nonstrict Feedback Form

Department of Mathematics and Computational Science, Huainan Normal University, 238 Dongshan West Road, Huainan 232038, China

Received 22 January 2014; Revised 27 March 2014; Accepted 13 April 2014; Published 29 April 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Yeguo Sun and Heng Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a fuzzy adaptive control method for MIMO uncertain chaotic systems in nonstrict feedback form, which is capable of guaranteeing the prescribed performance bounds. For the prescribed performance bounds, we mean that the tracking error should converge to a predefined arbitrarily small set, with convergence rate no more than a prescribed value. A novel output error transformation is introduced to transform the original constrained system into an equivalent unconstrained one, and it is proved that the stabilization of the unconstrained system is sufficient to solve the problem. Based on the error transformation technique, a fuzzy adaptive controller is designed for the unconstrained system. For updating the parameters of the fuzzy logic systems, a proportional-integral adaptation law is proposed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.