Stabilization of Unstable Periodic orbits of Chaotic Discrete-Time Systems Using Prediction-Based Feedback Control

In this paper, we consider feedback control that stabilizes unstable periodic orbits (UPOs) of chaotic discrete-time systems. First, we show that there exists a strong necessary condition for stabilization of the UPOs when we use delayed feedback control (DFC) that is known as one of the useful methods for controlling chaotic systems. The condition is similar to that in the fixed point stabilization problem, in which it is impossible to stabilize the target unstable fixed point if the Jacobian matrix of the linearized system around it has an odd number of real eigenvalues greater than unity. In order to stabilize UPOs which cannot be stabilized by the standard DFC, we adopt prediction-based control. We show a necessary and sufficient condition for the stabilization of the UPOs with arbitrary period.