基于分数阶滑模面控制的分数阶超混沌系统的投影同步

本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性. 关键词： 分数阶滑模面滑模控制器 稳定性分析 分数阶超混沌系统 投影同步

Fractional sliding mode surface controller for projective synchronization of fractional hyperchaotic systems

In this paper, a sliding mode controller with fractional sliding surface is designed for projective synchronization (PS) of fractional hyperchaotic systems via active control theory and sliding mode theory. The existence and the stability of PS between two fractional hyperchaotic systems are studied based on Lyapunov theory, fractional stability theory and the theory of fractional calculus. The criterions for the practical stability of the PS error system are presented also. Numerical simulation of PS between fractional Chen system and a new hyperchaotic system shows the effectiveness of the proposed controller law.