STABILIZING THE UNSTABLE PERIODIC ORBITS OF A CHAOTIC SYSTEM USING ADAPTIVE TIME-DELAYED STATE FEEDBACK

In this paper we deal with the control of chaotic systems. Knowing that a chaotic attractor contains a myriad of unstable periodic orbits (UPO's), the aim of our work is to stabilize some of the UPO's buried in the chaotic attractor and which have interesting characteristics. First, using the input-to-state linearization method in conjunction with a time-delayed state feedback, we design a control signal that can achieve stabilization. Next, an adaptive time-delayed state feedback is proposed which shows at once efficiency and simplicity. The efficacy of the proposed methods is illustrated by numerical simulations onto Chua's system.