Synchronization of Uncertain General Fractional Unified Chaotic Systems via Finite-Time Adaptive Sliding Mode Control

This chapter employs two adaptive sliding mode control (ASMC) strategies to accomplish finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) when uncertainty and external disturbance exist. Firstly, general fractional unified chaotic system (GFUCS) is developed. GFUCS may be transitioned from general Lorenz system to general Chen system, and general kernel function could compress and extend the time domain. Furthermore, two ASMC methods are applied to finite-time synchronization of UGFUCSs, where system states arrive at sliding surfaces in finite time. The first ASMC approach utilizes three sliding mode controllers to achieve synchronization between chaotic systems, while the second ASMC method needs just one sliding mode controller to produce synchronization between chaotic systems. Finally, the effectiveness of the proposed ASMC approaches is verified using numerical simulations.