Fast Learning Algorithm for Controlling Logistic Chaotic System Based on Chebyshev Neural Network

A novel algorithm for controlling Logistic chaotic system based on Chebyshev neural network (Chebyshev-NN) is presented. In the algorithm, Chebyshev orthogonal polynomials are applied to activation function of neural network, the forecasting and controlling model of logistic chaotic system is established. In order to ensure stability of the network, the convergence theorem of the network is proposed and proved. The Chebyshev neural network directly learns dynamic characters of logistic chaotic system and controls it to target function. The simulation results show that the algorithm is still effective when there are external disturbance in the logistic chaotic system. Compared with other ordinary algorithms, the algorithm has some merits including significantly little amount, fast convergence rate, high accuracy and simple network structure.