Robust finite-time synchronization of non-identical fractional-order hyperchaotic systems and its application in secure communication

Abstract

This paper proposes a novel adaptive sliding mode control &#x0028 SMC &#x0029 method for synchronization of non-identical fractional-order &#x0028 FO &#x0029 chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller &#x0028 ASMC &#x0029. Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization &#x0028 PSO &#x0029 is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.