Control of Chaotic Systems with Uncertainties by Orthogonal Function Neural Network

The adaptive control method based on orthogonal function neural network is proposed for a class of chaotic nonlinear systems. The adaptive controller is constructed by using a single hidden layer Chebyshev orthogonal function neural network which has advantages such as simple calculation and fast convergence. The adaptive learning law of orthogonal neural network is derived to guarantee that the adaptive weight errors and the tracking error are bounded from Lyapunov stability theory. The uncertain nonlinear system with the external disturbances can track the desired reference trajectory with bounded errors by means of the adaptive feedback controller. Based on the orthogonal function neural network, the control of chaotic systems with uncertainties is studied. The results show that the approach proposed in this paper can overcome effectively the external disturbances.