Adaptive fuzzy wavelet neural controller design for chaos synchronization

Chaotic system is a nonlinear deterministic system that displays complex, noisy-like and unpredictable behavior, so how to synchronize chaotic system become a great deal in engineering community. In this paper, an adaptive fuzzy wavelet neural synchronization controller (AFWNSC) is proposed to synchronize two nonlinear identical chaotic gyros. The proposed AFWNSC system is composed of a neural controller and a fuzzy compensator. The neural controller uses a fuzzy wavelet neural network to online approximate an ideal controller and the fuzzy compensator is used to guarantee system stable without chattering phenomena. All the parameter learning algorithms of the proposed AFWNSC scheme are derived in the Lyapunov stability sense. Finally, some simulation results verify the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized by the proposed AFWNSC scheme after learning of the controller parameters. Moreover, the convergence of the tracking error and control parameters can be accelerated by the developed proportional-integral type adaptation learning algorithm.