| 一类3D混沌系统的异宿轨道和backstepping控制 |
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| 引用本文： | 王震,李永新,惠小健,吕雷.一类3D混沌系统的异宿轨道和backstepping控制[J].物理学报,2011,60(1):10513-010513. |
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| 作者姓名： | 王震 李永新 惠小健 吕雷 |
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| 作者单位： | 西京学院基础部,西安 710123 |
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| 基金项目： | 西京学院科研基金(批准号:090107)资助的课题. |
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| 摘 要： | 基于异宿轨道Shilnikov准则,分析了一类三维自治微分系统异宿环的存在性,并证明了该系统具有Smale马蹄意义的混沌.然后对系统的分岔,Lyapunov指数,Poincare映射进行了数值分析,同时利用自适应反步控制方法,对含有三个未知参数的系统给出了一种控制算法.最后通过数值示例进行仿真,对文中论述进行了验证.
关键词：
异宿环
自适应反步
Shilnikov准则
Poincare映射
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| 关 键 词： | 异宿环 自适应反步 Shilnikov准则 Poincare映射 |
| 收稿时间： | 2009-12-26 |
Heteoclinic orbit and backstepping control of a 3 D chaotic system |
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| Wang Zhen,Li Yong-Xin,Xi Xiao-Jian,Lü Lei.Heteoclinic orbit and backstepping control of a 3 D chaotic system[J].Acta Physica Sinica,2011,60(1):10513-010513. |
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| Authors: | Wang Zhen Li Yong-Xin Xi Xiao-Jian Lü Lei |
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| Institution: | Department of Foundation, Xijing University, Xi'an 710123, China;Department of Foundation, Xijing University, Xi'an 710123, China;Department of Foundation, Xijing University, Xi'an 710123, China;Department of Foundation, Xijing University, Xi'an 710123, China |
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| Abstract: | The existence of heteoclinic loop which connects the saddle focus equilibrium points is analyzed for a three-dimensional differential system based on heteoclinic orbit Shilnikov method, which proves the system possesses "horseshoe" chaos. Then the system bifurcation, Lyapunov exponent, Poincare mapping are studied by numerical analysis. In addition, adaptive backstepping design is used to control this system with three unknown key parameters, and an algorithm of this controller is presented. Finally, we make some numerical simulations of the system in order to verify the analytic results. |
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| Keywords: | heteoclinic loop adaptive backstepping Shilnikov criterion Poincare mapping |
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