A new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controller structure to synchronize fractional-order chaotic systems with uncertainty and disturbances

This study presents a new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controllers to synchronize fractional-order chaotic systems with uncertainties and affected by disturbance. According to the proposed control approach, a new fractional order control law is presented which ensures robust and stable synchronization of chaotic systems in the presence of uncertainties of the master and slave systems and bounded disturbance according to Lyapunov theorem. The proposed sliding mode controller is used to synchronize two non-smooth chaotic jerk systems affected by disturbance and uncertainty. Simulation results verify effectiveness and robustness of the proposed control law.