|本期目录/Table of Contents|

[1]陈娟.采样数据P型迭代学习下非线性系统的收敛分析[J].集美大学学报(自然科学版),2025,(3):292-298.
　CHEN Juan.Convergence Analysis of Nonlinear Systems Under Sampled-Data P-Type Iterative Learning[J].Journal of Jimei University,2025,(3):292-298.
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采样数据P型迭代学习下非线性系统的收敛分析(PDF)
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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:
期数:
2025年第3期
页码:
292-298
栏目:
数理科学与信息工程
出版日期:
2025-05-28

文章信息/Info

Title:
Convergence Analysis of Nonlinear Systems Under Sampled-Data P-Type Iterative Learning
作者:
陈娟
集美大学理学院，福建 厦门 361021
Author(s):
CHEN Juan
School of Science,Jimei University,Xiamen 361021,China
关键词:
迭代学习控制; 收敛性; 采样数据系统; 非线性系统
Keywords:
iterative learning control; convergence; sampled-data systems; nonlinear systems
分类号:
-
DOI:
-
文献标志码:
A
摘要:
基于采样数据P型迭代学习控制下非线性系统，提出一种新的收敛分析方法。该方法将数学归纳法（MI）与压缩映射原理(CMP)相结合，以证明系统变量的有界性和有限迭代时跟踪误差的有界收敛性。然后利用反证法(PBC)以及MI-CMP进一步证明了任何迭代中跟踪误差的鲁棒收敛性，该收敛性与迭代变化不确定性和采样周期的边界相关。通过一阶线性系统的数值仿真，所提方法在5次迭代内实现跟踪误差从0.5至0.000 8的指数收敛，且控制输入始终有界，验证了理论的有效性和工程实用性。
Abstract:
This paper studies the nonlinear systems based on sampled-data P-type iterative learning control and proposes a new convergence analysis method.The method combines mathematical induction（MI）and the contraction mapping principle (CMP) to prove the boundary of system variables and the bounded convergence of the tracking errors in a finite number of iterations.Then,using the method of contradiction (PBC) and MI-CMP,it further proves the robust convergence of the tracking errors in any iteration,which is related to the uncertainty of iteration variation and the boundary of sampling period.Through numerical simulations on a first-order linear system,the proposed method achieves exponential convergence of the tracking errors from 0.5 to 0.000 8 within 5 iterations,while ensuring bounded control inputs,thereby validating both the theoretical effectiveness and engineering practicality.

参考文献/References:

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备注/Memo

备注/Memo:
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更新日期/Last Update: 2025-06-16