迭代学习控制的最优学习律和简化学习律的频域研究

doi:10.11896/j.issn.1002-137X.2019.02.050

计算机科学 ›› 2019, Vol. 46 ›› Issue (2): 327-332.doi: 10.11896/j.issn.1002-137X.2019.02.050

• 交叉与前沿 • 上一篇

迭代学习控制的最优学习律和简化学习律的频域研究

刘加存¹, 赵桂艳¹, 梅其祥²

广东海洋大学电子与信息工程学院广东湛江524088¹
广东海洋大学数学与计算机学院广东湛江524088²

收稿日期:2017-12-19 出版日期:2019-02-25 发布日期:2019-02-25
通讯作者: 赵桂艳(1975-),女,博士生,讲师,主要研究方向为智能控制、计算机检测,E-mail:zhaog19974@126.com
作者简介:刘加存(1962-),男,硕士,副教授,主要研究方向为智能控制、信号处理,E-mail:zjouljc@126.com;梅其祥(1973-),男,博士,副教授,主要研究方向为信息安全、信号处理。
基金资助:
本文受国家自然科学基金(61272534)资助。

Study of Optimal Learning Law and Simplified Learning Law of Iterative Learning Control in Frequency Domain

LIU Jia-cun¹, ZHAO Gui-yan¹, MEI Qi-xiang²

Faculty of Electrics and Information Engineering,Guangdong Ocean University,Zhanjiang,Guangdong 524088,China¹
Faculty of Mathematics and Computer Science,Guangdong Ocean University,Zhanjiang,Guangdong 524088,China²

Received:2017-12-19 Online:2019-02-25 Published:2019-02-25

摘要/Abstract

摘要： 为了在线性时不变MIMO系统中得到迭代学习控制的最优学习律和便于工程实现的简化学习律,在频域上对其进行了相关研究。以系统的传递函数矩阵为基础,依据Parseval定理,将时域误差关联为频域误差,再利用Jordan标准形矩阵等矩阵性质,得到了学习律的通适收敛条件。通过分析该条件,得出了收敛速度最快的一次迭代就能完成的最优学习律。由于高阶导数不利于消除噪音,因此文中还讨论了导数的降阶,给出了简化学习律算法。仿真结果表明,最优学习律和简化学习律是有效的。

关键词: 迭代学习控制, 频域, 收敛速度, 最优学习律

Abstract: To obtain the optimal learning law and simplified learning law which is convenient for engineering implementation of iterative learning control in LTI MIMO system,this paper carried out some studies in frequency domain.Based on the transfer function matrix of system,the time-domain error is converted to frequency-domain error according to Parseval theorem,and the general convergent condition of learning law can be obtained by using matrix properties of Jordan canonical form.The optimal learning law which needs only one time iterative computation with fastest convergence rate can be got by analyzing the aforementioned conditions.Since the higher derivative is not conducive to eliminating noise,the reduced order of derivative was discussed to get a simplified learning law.Simulation results show that the optimal and simplified learning law is effective.

Key words: Convergent rate, Frequency domain, Iterative learning control, Optimal learning law

中图分类号:

TP13

刘加存, 赵桂艳, 梅其祥. 迭代学习控制的最优学习律和简化学习律的频域研究[J]. 计算机科学, 2019, 46(2): 327-332. https://doi.org/10.11896/j.issn.1002-137X.2019.02.050

LIU Jia-cun, ZHAO Gui-yan, MEI Qi-xiang. Study of Optimal Learning Law and Simplified Learning Law of Iterative Learning Control in Frequency Domain[J]. Computer Science, 2019, 46(2): 327-332. https://doi.org/10.11896/j.issn.1002-137X.2019.02.050

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迭代学习控制的最优学习律和简化学习律的频域研究

Study of Optimal Learning Law and Simplified Learning Law of Iterative Learning Control in Frequency Domain

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