Fractional-order adaptive terminal sliding mode control for synchronization of uncertain chaotic memristive Chua's circuit

Abstract

Memristive-based chaotic dynamical systems exhibit chaotic behavior with signals of unpredictable complexity, making it difficult to achieve full synchronization in master-slave systems. Therefore, an advanced synchronization method is required to overcome the chaotic model uncertainties and external disturbances. In this study, a fractional-order terminal sliding mode synchronization is proposed for the uncertain memristive chaotic Chua's circuit. After presenting the integer-order model of the chaotic memristive Chua's circuit, a fractional-order sliding surface-based nonlinear synchronization structure, incorporating the fractional derivative operator, is designed. The convergence of the synchronization closed-loop system is proven using Lyapunov theory. To demonstrate its effectiveness and applicability, the proposed controller structure with a fractional-order surface is compared with three different control structures, and computer-based numerical simulation studies are presented.