基于分数阶滑模控制器的不确定分数阶混沌系统同步  

Synchronization of Uncertain Fractional-order Chaotic Systems Based on the Fractional-Order Sliding Mode Controller

作　　者：阎晓妹[1] 尚婷[1] 赵小国[2] YAN XIAOMEI;SHANG TING;ZHAO XIAOGUO(Faculty of Automation and Information Engineering, Xi'an University of Technology,Xi'an 710048,China;School of Mechanical and Electrical Engineering, Xi'an University of Architecture and Technology,Xi'an 710055,China)

机构地区：[1]西安理工大学自动化与信息工程学院,西安710048 [2]西安建筑科技大学机电工程学院,西安710055

出　　处：《应用数学学报》2018年第6期765-776,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61575158);陕西省教育厅科技研究计划专项(17JK0456)资助项目

摘　　要：针对具有建模误差和外部干扰的不确定分数阶混沌系统的同步问题,本文通过将分数阶到达律引入滑模控制,提出了一个新型的分数阶滑模控制器.基于Lyapunov稳定理论和分数阶系统稳定理论,分析了被控系统的稳定性.分别以两个分数阶Lü混沌系统间的同结构同步和分数阶Lü与分数阶Liu混沌系统间的异结构同步为例进行了数值仿真,仿真结果表明了该控制器的有效性和鲁棒性.For synchronization of uncertain fractional-order chaotic systems with model uncertainties and external disturbances,this paper presents a novel fractional-order sliding mode controller.The fractional-order controller is designed by introducing fractional order reaching law into sliding mode control.Based on Lyapunov stability theory and stability the- orem of fractional-order system,the controlled system's stability is analyzed.Two examples are successfully performed respectively,which include two identical fractional-order systems (Lü-Lü)and two non-identical fractional-order systems (Lü-Liu).Numerical simulations illustrate the effectiveness and the robustness of the proposed controller.

关 键 词：分数阶 滑模控制 混沌同步 不确定 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]