| 分片线性逼近的动态特性分析 |
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| 引用本文： | 牟晓牧,黄晓霖,王书宁.分片线性逼近的动态特性分析[J].清华大学学报(自然科学版),2011(7):879-883. |
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| 作者姓名： | 牟晓牧 黄晓霖 王书宁 |
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| 作者单位： | 清华大学自动化系; |
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| 基金项目： | 国家自然科学基金项目(61074118,60974008); 高等学校博士学科点科研基金(200800030029) |
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| 摘 要： | 为了合理地应用分片线性逼近方法解决非线性动态系统问题,对非线性动态特性在分片线性逼近下的一致性问题展开研究。在对典型的混沌映射Logistic映射进行分片线性逼近时,分片线性系统会表现出一些不同于原系统的动态特性。即使在静态逼近精度很高的情况下,逼近所得的分片线性系统的分岔图与原系统的分岔图也会有很大的差异。分析表明分片线性系统与原系统光滑性的差异是导致动态特性差异的原因。继而使用光滑化的分片线性模型作逼近,逼近结果的动态特性能够保持与原系统一致。光滑化的分片线性模型适用于逼近非线性动态系统。
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| 关 键 词： | 非线性动力学 分片线性逼近 Logistic映射 光滑链接超平面 |
Dynamic behavior of piecewise-linear approximations |
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| MU Xiaomu,HUANG Xiaolin,WANG Shuning.Dynamic behavior of piecewise-linear approximations[J].Journal of Tsinghua University(Science and Technology),2011(7):879-883. |
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| Authors: | MU Xiaomu HUANG Xiaolin WANG Shuning |
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| Institution: | MU Xiaomu,HUANG Xiaolin,WANG Shuning(Department of Automation,Tsinghua University,Beijing 100084,China) |
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| Abstract: | The use of piecewise-linear approximations to model nonlinear dynamic systems depends on the dynamic behavior of the piecewise-linear approximations.When the piecewise-linear approximation technique is used here to model the Logistic map,differences in the dynamic behavior are found between the approximation model and the original system.Even when the static error is very small,there are obvious differences between the bifurcation diagram of the original system and that of the piecewise-linear approximation... |
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| Keywords: | nonlinear dynamics piecewise-linear approximation Logistic map smoothed hinging hyperplane |
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