一类不确定分数阶舰船运动混沌系统的滑模同步控制  

Sliding model synchronization control of a class of uncertain fractional-order ship steering chaos systems

作　　者：程春蕊[1] 毛北行[1] CHENG Chunrui;MAO Beixing(School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450015, 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

出　　处：《安徽大学学报（自然科学版）》2021年第5期45-48,共4页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金青年基金资助项目(11801528);河南省高等学校重点科研基金资助项目(17A110034)。

摘　　要：运用Lyapunov稳定性理论和分数阶微积分的性质,研究一类不确定分数阶舰船运动混沌系统的同步控制问题,提出一种自适应滑模控制方法.通过设计分数阶非奇异终端滑模面和构造分数阶Lyapunov函数,证明在滑模面上误差系统能够稳定到平衡点;为了将同步误差系统的轨迹驱动到滑模面上,引入自适应滑模控制律,实现了主从系统的混沌同步;通过算例说明该方法的适用性,并验证了理论结果.This paper studied the synchronization of a class of uncertain fractional-order ship steering chaos systems based on Lyapunov stability theory and the properties of fractional calculus.And an adaptive sliding mode control strategy was proposed.A non-singular fractional-order terminal sliding surface was introduced and a fractional-order Lyapunov function was created to demonstrate the convergence to the equilibrium of the error dynamics in the sliding mode.A proper adaptive control law was then proposed to force the trajectory of the synchronization error systems onto the sliding surface.The chaos synchronization was thus achieved for master-slave systems.Numerical simulations were presented to illustrate the applicability of the proposed controller and to validate the theoretical results of the paper.

关 键 词：分数阶系统 舰船混沌运动 滑模 混沌同步 

分 类 号：O482.4[理学—固体物理]