Optimal Projective Synchronization of Non-identical Fractional-Order Chaotic Systems with Uncertainties and Disturbances Using Fractional Sliding Mode Control with GA and PSO Algorithms

This work presents an optimal projective synchronization of non-identical fractional-order chaotic systems (FOCS) in the presence of uncertainties and external disturbances using a fractional sliding mode controller (FSMC). For the first time, and based on Lyapunov stability theory, fractional-order sliding surfaces are proposed to design signal controllers for forcing errors behavior to zero and to make the states of the FOCS asymptotically stable. Then, to obtain optimal control parameters, GA and PSO algorithms will be introduced. An example of non-identical FOCS are proposed to demonstrate the effectiveness of the proposed optimal FSMC approach compared with the integer one. The simulation results show the applicability and efficiency of the proposed scheme.