Design of Adaptive Wavelet Neural Control System for Chaos Synchronization with Uncertainties

Chaotic dynamic system is a nonlinear deterministic system that displays complex, noisy-like and unpredictable behavior. Control and synchronization of chaotic dynamical system have attracted a great deal of attention within the engineering community. This paper proposes an adaptive wavelet neural control (AWNC) system to synchronize two identical chaotic gyros with nonlinear damping globally. The proposed AWNC system is composed of a neural controller and a robust controller. The neural controller uses a wavelet neural network (WNN) to approximate an ideal controller, and the robust controller is designed to dispel the effect of approximation error introduced by neural controller. The main advantage of the WNN is its fast learning rate compared to other neural networks due to it can provide more potential to enrich the mapping relationship between inputs and outputs. The parameter learning algorithm online adjusts the interconnection weights of WNN based on the Lyapunov function, thus the system’s stability can be guaranteed. Simulation results verify the chaotic behavior of two nonlinear gyros can be synchronized by the proposed AWNC scheme with fully unknown control system dynamics. The major contributions of this paper are: (1) to solve the problems of requirement of system models and uncertainty bound in the SMC (2) to eliminate the chattering phenomenon in the control effort and (3) the successful applications of the AWNC system to achieve accurate chaos synchronization control in gyros chaotic system.