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.