Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control

Abstract

• The synchronization of second-order chaotic systems is investigated. • A novel fixed-time adaptive sliding mode control scheme is proposed. • A new type of fixed-time nonsingular sliding mode surface is developed. • The semi-global fixed-time stability of the resulting closed-loop system is proved. In this paper, a novel fixed-time adaptive sliding mode control scheme is proposed for the synchronization of second-order chaotic systems with system uncertainties and external disturbances. First, a new type of fixed-time nonsingular sliding mode surface is developed based on the bi-limit homogeneous theory. Then, on the basis of the fixed-time sliding mode surface, the fixed-time adaptive sliding mode controller is designed by integrating the fixed-time terminal sliding mode control with the parametric adaptation technique. Finally, rigorous theoretical analysis for the semi-global fixed-time stability of the resulting closed-loop system is provided. A distinct feature of the proposed controller is that it can guarantee the synchronization tracking errors converge to the arbitrarily small neighbourhood of zero in fixed time even in the presence of lumped disturbances. To the best of the authors’ knowledge, there are relatively few existing controllers can achieve such excellent performance in the same conditions. Two simulation examples are performed to illustrate the effectiveness and benefits of the proposed control scheme.