Controlling chaos with weak periodic signals optimized by a genetic algorithm

In the present study we develop a relatively novel and effective chaos control approach with a multimode periodic disturbance applied as a control signal and perform an in-depth analysis on this nonfeedback chaos control strategy. Different from previous chaos control schemes, the present method is of two characteristic features: (1) the parameters of the controlling signal are optimized by a genetic algorithm (GA) with the largest Lyapunov exponent used as an index of the stability, and (2) the optimization is justified by a fitness function defined with the target Lyapunov exponent and the controlling power. This novel method is then tested on the noted Rössler and Lorenz systems with and without the presence of noise. The results disclosed that, compared to the existing chaos control methods, the present GA-based control needs only significantly reduced signal power and a shorter transient stage to achieve the preset control goal. The switching control ability and the robustness of the proposed method for cases with sudden change in a system parameter and/or with the presence of noise environment are also demonstrated.