新型分数阶混沌系统滑模同步的两个方案  

Two Schemes for Sliding Mode Synchronization of a New Fractional Order Chaotic System

作　　者：李庆宾[1] 毛北行[1] 薛均晓[2] LI Qing-bin;MAO Bei-xing;XUE Jun-xiao(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China;School of Software,Zhengzhou University,Zhengzhou 450002,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450015 [2]郑州大学软件学院,河南郑州450002

出　　处：《数学的实践与认识》2020年第23期197-201,共5页Mathematics in Practice and Theory

基　　金：河南省自然科学基金(162300410262);河南省高等学校重点科研项目(18A413002)。

摘　　要：利用滑模同步方法,研究了一种新型分数阶混沌系统的滑模同步问题.基于分数阶微积分相关结论和李雅普诺夫稳定性理论,分别设计了两种不同的滑模面与控制器,通过合理设计切换函数和控制律,可以使误差系统沿着滑模面滑动并最终趋于稳定,从而主从系统取得同步.最后,应用MATLAB进行数值仿真,结果表明在设计的滑模面和控制器作用下,分数阶混沌系统可以在非常短的时间内取得滑模同步.The problem of chaos synchronization of a new fractional order chaotic system is studied by using the sliding mode synchronization method.Based on the conclusion of fractional calculus and Lyapunov stability theory,two kinds of sliding surfaces and controllers are designed respectively.By properly designing the switching function and control law,the error system can slide along the sliding surface and finally become stable,so that the masterslave systems can achieve synchronization.Finally,the numerical simulation with MATLAB shows that the fractional order chaotic system can achieve sliding mode synchronization in a very short time under the designed sliding mode surface and controller.

关 键 词：分数阶系统 滑模控制 混沌同步 

分 类 号：O415.5[理学—理论物理]