Lyapunov Exponent-based PI Optimization for the Delayed Feedback Control of Chaos

The objective of this study is the control and stabilization of chaotic systems. It proposes a new hybrid control approach combining the proportional-integral (PI) technique with the delayed feedback control approach. The main idea behind this is to transform the structural stabilization problem into an optimization task. The target is to find the PI gains optimal values that give the lowest value for the maximum Lyapunov exponent. The PI argument is the difference between the present state of the system and its delayed value by one period. This allows the optimal structural stabilization of the chaotic orbits of the system. The widening of the stable region, and the decrease of the transient time for stabilization. The proposed approach is validated, and its performance is shown by numerical simulation on a chaotic system benchmark.