On the prediction of chaotic time series using a new generalized radial basis function neural networks

Radial basis function (RBF) networks have been widely used for function approximation and pattern classification as an alternative to conventional feedforward neural networks. A novel generalized RBF neural network model is presented. The form of RBF is determined by a generator function, and then an easily implementable gradient decent learning algorithm for training the new generalized RBF networks is given. Simultaneously, a fast dynamic learning algorithm based on Kalman filter is also proposed to improve the performance and accelerate the convergence speed of the new generalized RBF networks. The generalized RBF neural networks based on Kalman filtering dynamic learning algorithm is then applied to the chaotic time series prediction on the Mackey-Glass equation and the Henon map to test the validity of this proposed model. Simulation results show that the new generalized RBF networks can accurately predict chaotic time series. It provides an attractive approach to study the properties of complex nonlinear system model and chaotic time series.