Stable predictive control of chaotic systems using self-recurrent wavelet neural network

In this paper, a predictive control method using self-recurrent wavelet neural network (SRWNN) is proposed for chaotic systems. Since the SRWNN has a self-recurrent mother wavelet layer, it can well attract the complex nonlinear system though the SRWNN has less mother wavelet nodes than the wavelet neural network (WNN). Thus, the SRWNN is used as a model predictor for predicting the dynamic property of chaotic systems. The gradient descent method with the adaptive learning rates is applied to train the parameters of the SRWNN based predictor and controller. The adaptive learning rates are derived from the discrete Lyapunov stability theorem, which are used to guarantee the convergence of the predictive controller. Finally, the chaotic systems are provided to demonstrate the effectiveness of the proposed control strategy.