An Adaptive Neural Network Control Scheme for Stabilizing Chaos to the Stable Fixed Point

Abstract

A neural network control scheme with a novel adaptive learning rate is proposed to stabilize the chaotic trajectory of the chaotic system to a stable fixed point. A new approach is proposed to determine the stability of the fixed points in which the eigenvalues of the Jacobian matrix of the chaotic system at different values of the chaoticity parameter are evaluated and a look-up table is created to find a suitable fixed point that has a negative Lyapunov exponent. During learning phase of the neural network, weight parameters are adjusted so that the chaotic trajectory converges to a stable fixed point and the maximum Lyapunov exponent of the controlled system becomes negative. The effectiveness of the proposed method is investigated through simulation studies on 2 dimensional Ikeda map, which is produced by a semiconductor laser system.