Chaos control on autonomous and non-autonomous systems with various types of genetic algorithm-optimized weak perturbations

Recently, we proposed a chaos control strategy with weak Fourier signals optimized by using a genetic algorithm (GA) and demonstrated its merits in controlling Lorenz and Rössler systems (Physical Review E, 2004). In this continuation work, performance of various types of signals, namely periodic continuous, periodic discrete, and constant bias (non-periodic), applied to an autonomous (Rössler) system and a non-autonomous (Murali–Lakshmanan–Chua, MLC) system are investigated. An index of relative robustness is proposed for measuring the noise-resisting ability of the control signals. The results reveal that the constant signal has the strongest noise-resisting ability, the periodic pulse signal has the weakest, and the Fourier signal falls in between. Phase modulation generally shortens the transient time period and is additionally beneficial to non-autonomous systems in minimizing significantly the signal power. By searching with the present GA-optimization, it is demonstrated that the minimum-power signal for controlling the non-autonomous (MLC) system is the signal with a frequency exactly the same as that of the system forcing but with phase modulation. The effectiveness of the GA-optimized signals of extremely low power employed in alternatively switching control of non-autonomous systems is also demonstrated.