Controlling chaos by GA-based reinforcement learning neural network.

This paper proposes a TD (temporal difference) and GA (genetic algorithm) based reinforcement (TDGAR) neural learning scheme for controlling chaotic dynamical systems based on the technique of small perturbations. The TDGAR learning scheme is a new hybrid GA, which integrates the TD prediction method and the GA to fulfill the reinforcement learning task. Structurely, the TDGAR learning system is composed of two integrated feedforward networks. One neural network acts as a critic network for helping the learning of the other network, the action network, which determines the outputs (actions) of the TDGAR learning system. Using the TD prediction method, the critic network can predict the external reinforcement signal and provide a more informative internal reinforcement signal to the action network. The action network uses the GA to adapt itself according to the internal reinforcement signal. This can usually accelerate the GA learning since an external reinforcement signal may only be available at a time long after a sequence of actions have occurred in the reinforcement learning problems. By defining a simple external reinforcement signal, the TDGAR learning system can learn to produce a series of small perturbations to convert chaotic oscillations of a chaotic system into desired regular ones with a periodic behavior. The proposed method is an adaptive search for the optimum control technique. Computer simulations on controlling two chaotic systems, i.e., the Hénon map and the logistic map, have been conducted to illustrate the performance of the proposed method.