不确定扰动分数阶混沌系统自适应Terminal滑模同步

Synchronization of Uncertain Fractional Order Chaotic Systems with Disturbance Based on Adaptive Terminal Sliding Mode Control

针对带扰动不确定分数阶混沌系统的同步问题,基于自适应Terminal滑模控制,设计了一种分数阶非奇异Terminal滑模面,保证误差系统沿着滑模面在有限时间内稳定至平衡点,在系统外部扰动和不确定性的边界事先未知的情况,设计了自适应控制率,在线估计未知边界,使得同步误差轨迹能到达滑模面。最后,以三维分数阶Chen系统和四维分数阶Lorenz超混沌系统为例,利用所设计的自适应Terminal滑模控制器进行同步仿真,验证了所给方法是有效性和可行性。

In this paper, the problem of synchronization of uncertain fractional order chaotic systems with disturbance is investigated based on adaptive terminal sliding mode control method. Firstly, a new non-singular fractional order terminal sliding surface with strong robustness is designed to guarantee finite-time convergence to the equilibrium of the error dynamics in the sliding mode. Then,for the case that the bounds of the uncertainties and external disturbances are assumed to be unknown in advance, an adaptive control law is proposed to estimate the unknown bounds online, and force the trajectory of the synchronization error system onto the sliding surface. Finally,numerical simulations on synchronizing Chen chaotic system and hyperchaos Lorenz are carried out separately. The simulation results show the effectiveness and feasibility of the adaptive terminal sliding mode controller.