Adaptive Delayed Feedback Chaos Control of a Class of Uncertain Chaotic Systems Subject to External Disturbance

摘要

In this paper, an adaptive nonlinear delayed feedback control is proposed for stabilizing an unstable periodic orbit (UPO) of a class of uncertain chaotic systems using the sliding mode approach. The chaotic system is subjected to external disturbances with unknown bounds. Using the Lyapunov stability theorem and the concept of sliding mode control, an adaptive delayed feedback controller has been designed. The controller and adaptation law guarantee the asymptotic stability of the closed loop system on a periodic trajectory which can be sufficiently close to the UPO of the chaotic system. The capability of the proposed control method in stabilizing the UPO of chaotic systems is established analytically and the effectiveness of the proposed scheme is examined numerically by applying it to the chaotic Duffing and Gyro systems.