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Zbl 1139.93010
Tsai, Zhi-Ren; Chang, Yau-Zen; Hwang, Jiing-Dong; Lee, Jye
Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm.
(English)
[J] Inf. Sci. 178, No. 4, 1171-1188 (2008). ISSN 0020-0255

Summary: Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered $H_{\infty }$ robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient conditions for the existence of the $H_{\infty }$ robust fuzzy controllers are presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the Island-based Random-walk Algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.
MSC 2000:
*93B35 Sensitivity (robustness) of control systems
93C42 Fuzzy control
37D45 Strange attractors, chaotic dynamics
93D21 Adaptive and robust stabilization

Keywords: chaotic systems; dither; $H_{\infty }$ robust fuzzy control; linear matrix inequality

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