近似熵在小车一级倒立摆混沌边缘分析中的应用

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英文篇名：Applying Approximate Entropy to Analyze the Edge of Chaos of Inverted Pendulum on a Cart 作者：张猛 ; 谢进 ; 魏巍 ; 任必春 英文作者：ZHANG Meng,XIE Jin,WEI Wei,REN Bi-chun(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu,610031,China) 关键词：熵 ; 似熵 ; 立摆 ; 混沌 ; 混沌边缘 英文关键词：entropy;approximate entropy;inverted pendulum;chaos;edge of chaos 中文刊名：JZDF 英文刊名：Control Engineering of China 机构：西南交通大学机械工程学院; 出版日期：2013-05-20 出版单位：控制工程 年：2013 期：v.20 基金：国家自然科学基金资助项目(51175437) 语种：中文; 页：JZDF2013S1063 页数：4 CN：S1 ISSN：21-1476/TP 分类号：235-238

摘要

熵是一种衡量数据不规则性的方法,是少有的判断混沌现象的定量指标之一。研究的目的是探明机构混沌运动以及在其混沌运动边缘熵值的变化情况。以小车直线一级倒立摆为研究对象,通过动力学仿真提取系统的动力响应时间序列,利用近似熵的方法,研究了小车一级倒立摆混沌边缘近似熵值的变化情况。主要研究结论是在系统的动态响应从周期运动到混沌运动的变换过程中,近似熵也经历了从0到大于0的变化;而在混沌边缘,出现了近似熵在0与大于0之间的交替变化,说明此时系统的周期运动与混沌运动共存。本文利用相轨迹法验证了结论的正确性。
        Entropy is one of the approaches to measure the irregularity of a set of data.And it is one of the rare computable tests for chaos.Aiming at finding figuring out how the value of entropy varies when the motion of a mechanism become chaotic and at the edge of chaos and,the inverted pendulum on a cart,in this paper,is taken as an example in the paper.The time series of the response is extracted from the simulation of the dynamic model;approximate entropy is employed to analyzing analyze the variation of the values of entropy.It is shown that the approximate entropy undergoes a change from 0 to larger than 0 as the system changes from periodic motion to chaotic motion.And at the edge of chaos,the approximate entropy alternates between 0 and larger than 0,which means that periodic motion and chaotic motion coexist at the edge of chaos.The conclusions are proved by the phase diagrams of system.

引文

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