不确定Duffing混沌系统的有限时间同步

徐瑞萍1,2a， 高存臣2b

 （1.青岛大学 数学科学学院，山东 青岛 266071；

 2.中国海洋大学 a.信息科学与工程学院；b.数学科学学院，山东 青岛 266100）

摘要: 研究了带有不确定性和外部扰动的Duffing混沌系统在有限时间内的同步问题。提出一种基于双幂次趋近律的非奇异终端滑模控制策略。首先设计了非奇异终端滑模面，保证误差系统沿着滑模面在有限时间内稳定至平衡点；然后基于双幂次趋近律设计了控制器，使得同步误差轨迹能在有限时间内到达滑模面，从而实现了混沌系统的有限时间同步并有效地解决了终端滑模控制的抖振和收敛缓慢问题；最后，数值仿真结果说明所给方法的有效性。

关键词: Duffing混沌系统； 有限时间同步； 非奇异终端滑模； 双幂次趋近律

 中图分类号： TP 271;O 231.2              文献标志码： A

Finitetime Synchronization of Duffing Chaotic System with Uncertainty

XU Ruiping1,2a, GAO Cunchen2b

 (1.School of Mathematics Science, Qingdao University, Qingdao 266071, China；

2.a.School of Information Science and Engineering； b.School of Mathematical Sciences,

Ocean University of China, Qingdao 266100, China)

Abstract: The problem of finitetime synchronization between two Duffing systems with uncertainties and disturbances is investigated. On the basis of a double power reaching law, a nonsingular terminal sliding mode control algorithm is proposed. First, a new nonsingular terminal sliding surface is introduced to guarantee finitetime convergence to the equilibrium of the error dynamics in the sliding mode; Then, a controller is proposed based on a double power reaching law to force the trajectories of the synchronization error system onto the sliding surface in a given finite time and the finitetime synchronization conditions are obtained, and restrain chattering and improve convergence speed of terminal mode control effectively; Finally, simulation results are presented to illustrate the effectiveness of the design.

Key words: Duffing chaotic system; finitetime synchronization； nonsingular terminal sliding mode; double power reaching law

 收稿日期： 20140707

 基金项目： 国家自然科学基金项目（60974025）.

 作者简介： 徐瑞萍（1976—），女，博士，讲师.

文章编号： 16726987（2015）03035005； DOI： 10.16351/j.16726987.2015.03.023