Stabilizing unstable periodic orbits of chaotic systems via an optimal principle

A novel time-delayed control method is proposed for stabilizing inherent un stable periodic orbits (UPOs) in chaotic systems. Differing from the common ly used linear time-delayed feedback control form, we adopt an optimal cont rol principle for the design of the time delayed feedback control. We explo re 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 simu lations. (C) 2000 The Franklin Institute. Published by Elsevier Science Ltd . All rights reserved.