Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance

This paper studies the fractional-order disturbance observer (FODO)-based adaptive sliding mode synchronization control for a class of fractional-order chaotic systems with unknown bounded disturbances. To handle unknown disturbances, the nonlinear FODO is explored for the fractional-order chaotic system. By choosing the appropriate control gain parameter, the disturbance observer can approximate the disturbance well. On the basis of the sliding mode control technique, a simple sliding mode surface is defined. A synchronization control scheme incorporating the introduced sliding mode surface and the designed disturbance observer is then developed. Under the control of the synchronization scheme, a good synchronization performance is realized between two identical fractional-order chaotic systems with different initial conditions. Finally, the numerical simulation results illustrate the effectiveness of the developed synchronization control scheme for fractional-order chaotic systems in the presence of external disturbances.