Specified time dual-group synchronization of uncertain complex chaotic systems

Abstract

Aiming at the specified time dual-group synchronization problem of multi-wing complex chaotic systems containing uncertain terms and external disturbances, a new specified-time sliding mode control scheme is proposed, which directly synchronizes the complex chaotic system without separating the real and imaginary parts of the complex chaotic system. First, a new specified time stability criterion is used to construct the integral sliding mode surface of the synchronous error system to ensure stable sliding motion within the specified time. Subsequently, a proximity controller is designed to drive the error system to reach and remain on the sliding surface within another specified time, thereby achieving specified-time synchronization. In order to realize the proposed stability concept, this paper introduces a new sliding surface and defines the corresponding control law and adaptive rate. The effectiveness of this scheme is proved through Lyapunov stability theory and specified time stability theory. Numerical simulation results show that the scheme has strong robustness to uncertainties and external disturbances, and the controller is not affected by internal uncertainties and external disturbances. Compared to other stabilization time control schemes, this scheme has a shorter synchronization time. In general, this study introduces complex variables and adopts a scheme in which sliding mode surface parameters and controller parameters can be preset to simultaneously achieve dual-group synchronization of two groups of complex chaotic systems within the complex domain. This study offers greater flexibility, presenting novel ideas and approaches for the synchronization control of complex systems. It holds significant theoretical and practical value, providing valuable references and insights for research and applications in related fields.