Synchronization of uncertain general fractional unified chaotic systems via finite-time adaptive sliding mode control

This paper 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. First, general fractional unified chaotic system (GFUCS) is developed. GFUCS may be transitioned from general Lorenz system to general Chen system, and the 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.

Automated summary

This paper proposes two adaptive sliding mode control (ASMC) strategies for achieving finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) in the presence of uncertainty and external disturbance. The general fractional unified chaotic system (GFUCS) is first developed, which can be transitioned from the general Lorenz system to the general Chen system using a general kernel function. Two ASMC methods are then employed to achieve finite-time synchronization of UGFUCSs, where the system states reach the sliding surfaces within a finite time. The first ASMC approach uses three sliding mode controllers for synchronization between chaotic systems, while the second ASMC method only requires one sliding mode controller. The effectiveness of the proposed ASMC approaches is verified through numerical simulations.