Synchronizing Chaotic Systems with Uncertain Model and Unknown Interference Using Sliding Mode Control and Wavelet Neural Networks

A method using sliding mode control (SMC) and wavelet neural networks (WNN) is proposed, investigated and exploited for synchronizing master and slave chaotic systems with uncertain model and unknown interference. In this paper, integral sliding surface and applying WNN for approximating uncertain model and unknown interference are further developed for designing adaptive sliding mode controller. Mexican hat wavelet function is used as activation function in WNN. The adaptive laws of network parameters are derived in the sense of Lyapunov stability analysis so that the tracking errors and convergence of the weights can be guaranteed. The error of synchronization of master–slave chaotic systems can be reached desired level in limited time by using Li function in SMC. Illustrative examples are provided and analyzed to substantiate the efficacy of proposed method for solving the problem of synchronizing master and slave chaotic systems.