基于有限差分法的二阶双曲型分布参数系统的迭代学习控制

数学物理学报 ›› 2018, Vol. 38 ›› Issue (3): 588-598.

基于有限差分法的二阶双曲型分布参数系统的迭代学习控制

李向东, 傅勤, 吴健荣

苏州科技大学数理学院苏州 215009

收稿日期:2016-10-24 修回日期:2017-04-14 出版日期:2018-06-26 发布日期:2018-06-26
通讯作者: 傅勤 E-mail:fuqin925@sina.com
基金资助:
国家自然科学基金（11371013）和苏州科技大学自然科学基金项目（XKZ201613）

Iterative Learning Control for Second Order Hyperbolic Distributed Parameter Systems Based on Finite Differential Method

Li Xiangdong, Fu Qin, Wu Jianrong

School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009

Received:2016-10-24 Revised:2017-04-14 Online:2018-06-26 Published:2018-06-26
Supported by:
Supported by the NSFC (11371013) and the Natural Science Foundation of Suzhou University of Science and Technology (XKZ201613)

摘要/Abstract

摘要： 研究了一类分布参数系统基于有限差分法的迭代学习控制问题，该类分布参数系统由二阶双曲型偏微分方程所构建.针对系统所满足的初、边值条件，基于有限差分法构建得到迭代学习控制律，利用迭代收敛原理，证明这种学习律能使得系统的状态跟踪误差沿迭代轴方向收敛到原点的一个小邻域内.数值仿真验证了所提算法的有效性.

关键词: 双曲型分布参数系统, 学习律, 迭代学习控制, 有限差分法

Abstract: In this paper, the iterative learning control for distributed parameter systems based on finite differential method is considered. Here, the considered distributed parameter systems are composed of second order hyperbolic partial differential equations. According to the initialboundary conditions of the systems, iterative learning control laws are proposed based on finite differential method. Using the iterative converge principle, we show that the schemes can guarantee the state tracking errors can converge to a small region of the origin along the iteration axis. Finally, the simulation result verifies the effectiveness of the proposed algorithm.

Key words: Hyperbolic distributed parameter systems, Learning scheme, Iterative learning control, Finite differential method

中图分类号:

TP13

李向东, 傅勤, 吴健荣. 基于有限差分法的二阶双曲型分布参数系统的迭代学习控制[J]. 数学物理学报, 2018, 38(3): 588-598.

Li Xiangdong, Fu Qin, Wu Jianrong. Iterative Learning Control for Second Order Hyperbolic Distributed Parameter Systems Based on Finite Differential Method[J]. Acta mathematica scientia,Series A, 2018, 38(3): 588-598.

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