Stable Fractional-order Adaptive Sliding-based Control and Synchronization of two Fractional-order Duffing–Holmes Chaotic Systems

This study investigates the synchronization of a fractional-order adaptive sliding mode control strategy of two fractional-order Duffing–Holmes chaotic systems in the presence of uncertainty and disturbance using a fractional-order sliding surface. Initially, adaptive rules are used to estimate the boundaries of uncertainty and disturbance of the slave system. Subsequently, a novel fractional-order sliding surface is designed to synchronize the two systems. Finally, the slave system is tested to ensure it can successfully follow the master system. Using a fractional-order sliding surface, the proposed controller ensures the asymptotic stability of the synchronization error in the presence of uncertainties and disturbances. This approach reduces the adaptation time and improves the controller’s accuracy. The chattering phenomenon is eliminated using a tan function, which also leads to a very low steady-state error. The results depict that the proposed controller effectively synchronizes two chaotic systems.