Controlling chaos by RBF neural network based on GA optimization

A new kind of method is presented for controlling chaotic dynamical systems using RBF (radial basis function) neural network based on GA (genetic algorithm) (called GANN learning method). With the general-purpose stochastic search capability, GAs optimize the neural network´s structure parameters, and with the strong nonlinear approaching character, the neural network can learn to produce a series of small perturbations to convert chaotic oscillations of a dynamical system into a periodic orbit. An entirely unsupervised study strategy is adopted directly so that the system knowledge does not need to be realized in advance. In some real-world physical chaotic systems, it is difficult to determine the key parameters, so the proposed method can be applied to more practical situations. The algorithm convergence performance has been analyzed carefully and the severe proofs have been given. Computer simulations have also been conducted to control two chaotic systems, i.e., the Henon map and the logistic map. The results indicate that this method is efficient.