A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty

Abstract

In this paper, a class of integer and fractional-order chaotic systems, which undergoes external disturbances and system uncertainties, are considered. A robust synchronization scheme that incorporates a sliding mode controller established on a new fractional-order surface. A fractional order derivative provides an additional degree of freedom in the sliding surface. After that, the stability analysis for closed loop system is studied. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the synchronizing error to zero without any disturbance exerted upon the stability. The proposed method is designed for a wide class of chaotic systems. Furthermore, the results are extended for fractional-order version of chaotic systems. The proposed controller can be used to both integer and fractional order chaotic systems. The design is simple with rigorous stability analysis. Several numerical simulations are provided to verify the effectiveness of the theoretical results.