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Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm. (English) Zbl 1139.93010
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:
 93B35 Sensitivity (robustness) of control systems 93C42 Fuzzy control systems 37D45 Strange attractors, chaotic dynamics 93D21 Adaptive or robust stabilization