分数阶迭代学习控制的收敛性分析
Convergence analysis of fractional-order iterative learning control
摘要点击 1931  全文点击 1358  投稿时间:2012-05-08  修订日期:2012-06-27
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DOI编号  10.7641/j.issn.1000-8152.2012.8.LCTA120475
  2012,29(8):1031-1037
中文关键词  迭代学习控制  分数阶微积分  非线性系统  收敛性  自适应
英文关键词  iterative learning control  fractional calculus  nonlinear systems  convergence  adaptiveness
基金项目  This work was supported by the National Natural Science Foundation of China (Nos. 61075092, 61104009), and the Natural Science Foundation of Shandong Province (Nos. ZR2011FM011, ZR2010AM007).
作者单位E-mail
李岩 山东大学 控制科学与工程学院 liyan.sdu@gmail.com 
陈阳泉 加州大学默塞德分校 工程学院  
安孝晟 光州科学技术院 机械电子学系  
中文摘要
      本文将传统的迭代学习控制时域和频域分析方法扩展到一类针对分数阶非线性系统的分数阶迭代学习控制时域分析方法. 提出了一类新的分数阶迭代学习控制框架并简化了收敛条件, 且证明了常增益情况下两类分数阶迭代学习控制收敛条件的等价性问题. 该讨论进一步引出了如下两个结果: 分数阶不确定系统的分数阶自适应迭代学习控制的可学习区域以及理想带阻型分数阶迭代学习控制的框架. 上述结果均得到了仿真验证.
英文摘要
      The classical time domain and frequency domain analysis of iterative learning control (ILC) are extended to a type of time domain analysis of fractional order iterative learning control (FOILC) for fractional order nonlinear systems. A novel FOILC scheme is proposed, which leads to simpler convergence condition. The equivalence of the above two FOILC schemes is shown for the constant learning gain cases, which leads to two further developments: the learnable domain of an adaptive FOILC for the uncertain fractional order systems, and a desirable band-stop FOILC scheme. Several examples are provided to illustrate the presented results.