东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2006, Vol. 27 ›› Issue (8): 835-838.DOI: -

• 论著 • 上一篇    下一篇

迭代学习控制的收敛速度分析

朴凤贤;张庆灵;王哲峰;   

  1. 东北大学理学院;东北大学理学院;沈阳航空工业学院 辽宁沈阳110004;辽宁沈阳110004;辽宁沈阳110034
  • 收稿日期:2013-06-23 修回日期:2013-06-23 出版日期:2006-08-15 发布日期:2013-06-23
  • 通讯作者: Piao, F.-X.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(60574011);;

Analysis of convergence rate for iterative learning control

Piao, Feng-Xian (1); Zhang, Qing-Ling (1); Wang, Zhe-Feng (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) Shenyang Institute of Aeronautical Engineering, Shenyang 110004, China
  • Received:2013-06-23 Revised:2013-06-23 Online:2006-08-15 Published:2013-06-23
  • Contact: Piao, F.-X.
  • About author:-
  • Supported by:
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摘要： 针对线性时不变控制系统,讨论了D型和P型学习律收敛速度问题.利用时间加权范数和Frobenius范数给出了迭代学习控制系统在D型和P型学习律作用下收敛的充分性条件,进而给出系统迭代次数与约束条件之间的定量关系以及收敛速度与约束条件之间的关系,同时利用Frobenius范数性质,并通过梯度法给出如何求解D型和P型学习律使得系统收敛速度最快的增益矩阵的方法.最后,仿真实例说明了该方法的有效性.

关键词: 迭代学习控制, 时间加权范数, 学习律, 收敛速度

Abstract: The convergence rate is analyzed for both D-type and P-type learning laws in linear time-invariant control system. A sufficient condition is given by the Frobenius norm and time-weighted norm to guarantee the convergence of D-type and P-type learning laws. Furthermore, the quantitative relation between iterative number and the relation between convergence rate and constraint condition are given. Simultaneously, the approach to choosing the gain matrix for D-type/P-type learning law so as to get highest convergence rates is given by gradient flow and the property of Frobenius norm. Numerical simulation shows the effectiveness of the proposed method.

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