Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

Abstract

This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance