Stabilizing unstable periodic orbits of chaotic systems via an optimal principle

A novel time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems. Differing from the commonly used linear time-delayed feedback control form, we adopt an optimal control principle for the design of the time delayed feedback control. We explore the inherent properties of chaotic systems and use the system states and time-delayed system states in forming a performance index so that when the index is minimized, the resulting controller enables stabilization of the desired UPOs. The effectiveness of the method is confirmed by computer simulations.