基于PIα控制的分数阶超混沌Chen系统同步研究

Synchronization of fractional order hyperchaotic Chen system based on PIα control

本文提出一种PIα控制器设计方法,实现了分数阶超混沌Chen系统的混沌同步.首先针对分数阶超混沌Chen系统设计了PIα控制器,然后利用改进的双参数Mittag-Leffler函数估计定理和扩展的Gronwall引理证明了系统的稳定性,并指出了使分数阶超混沌Chen系统同步的控制器参数需满足的条件.仿真结果证实了所设计方法的有效性.

In this paper, a kind of PIα controller is designed for the synchronization of fractional order hyperchaotic Chen system. The controller is designed according to the fractional order hyperchaotic Chen system. The stability of the system is proved by the im- proved double parameter Mittag-Leffler function estimate theorem and the extended Gronwall lemma. Furthermore, the condition of controller parameters is pointed out which makes the fractional order hyperchaotic Chen system synchronous. Numerical simulations are presented to verify the effectiveness of the method.