不确定分数阶混沌系统的滑模投影同步

针对2阶不确定分数阶混沌系统的投影同步问题,提出基于滑模原理的同步控制方法.分数阶导数采用Caputo的定义.控制律由趋近控制和等价控制2部分组成.趋近控制采用指数趋近律,等价控制利用系统轨迹在滑模面上运动时滑模面的时间导数为零的条件得到.在控制器设计过程中,利用分数阶系统的Lyapunov理论分析滑模面的存在性,简化稳定性证明方法,得到了存在不确定性时分数阶系统达到同步的稳定性定理,实现了控制目标.通过对分数阶Duffing Holmes系统的完全状态投影同步的仿真,证明了该方法的有效性.

Projective synchronization of uncertain fractional order chaotic systemusing sliding mode controller

A sliding mode controller was proposed for the projective synchronization of second order fractional uncertain chaotic system. The Caputo’s fractional derivative was adopted. The total controller was composed of the approach controller and the equivalence controller. The exponent approach law was adopted for the approach controller. The equivalence controller was designed by using of the fact that the time derivative of the sliding surface is zero when the trajectory of the controlled system is on the surface. The existence of the sliding surface was analyzed and a simple stability analysis was obtained based on the Lyapunov theory for fractional differential system. Then the stability theorem for fractional system considering the uncertainty was provided and the synchronization aim was achieved. The simulation for the fractional chaotic uncertain Duffing Holmes system showed the effectiveness of the controller.