Synchronization of the Chaotic Fractional-Order Genesio–Tesi Systems Using the Adaptive Sliding Mode Fractional-Order Controller

This paper introduces an adaptive fractional-order sliding mode controller for synchronization of two chaotic Genesio–Tesi systems with fractional dynamics. For this purpose, first the error dynamics is defined; then the adaptive sliding mode synchronization controller is designed through defining suitable sliding surface and estimating uncertainty parameters and stability of the control system is verified using related theorems. Robustness against input uncertainty and disturbance is considered as a primary design objective. Simulation results using MATLAB show that the proposed adaptive fractional-order sliding mode controller is able to synchronize the mentioned chaotic system with acceptable performance.