Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

Abstract This paper proposes a modified adaptive sliding-mode control technique and investigates the reduced-order and increased-order synchronization between two different fractional-order chaotic systems using the master and slave system synchronization arrangement. The parameters of the master and slave systems are different and uncertain. These systems exhibit different chaotic behavior and topological properties. The dynamic behavior of the proposed synchronization schemes is more complex and unpredictable. These attributes of the proposed synchronization schemes enhance the security of the information signal in digital communication systems. The proposed switching law ensures the convergence of the error vectors to the switching surface and the feedback control signals guarantee the fast convergence of the error vectors to the origin. Lyapunov stability theory proves the asymptotic stability of the closed-loop. The paper also designs suitable parameters update laws the estimate the unknown parameters. Computer-based simulation results verify the theoretical findings.