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Adaptive synchronization of T-S fuzzy chaotic systems with unknown parameters. (English) Zbl 1092.37512
Summary: This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by an adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by the Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Duffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.

MSC:
37D45Strange attractors, chaotic dynamics
93D15Stabilization of systems by feedback
93D05Lyapunov and other classical stabilities of control systems
93D21Adaptive or robust stabilization
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References:
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