正则系统在Lebesgue-p范数意义下的快速迭代学习控制  

Fast iterative learning control for regular system in sense of Lebesgue-p norm

作　　者：曹伟[1] 李艳东[1] 王妍玮[2] CAO Wei;LI Yandong;WANG Yanwei(College of Computer and Control Engineering,Qiqihar University,Qiqihar Heilongjiang 161006,China;School of Mechnical Engineering,Harbin Institute of Petroleum,Harbin Heilongjiang 150027,China)

机构地区：[1]齐齐哈尔大学计算机与控制工程学院,黑龙江齐齐哈尔161006 [2]哈尔滨石油学院机械工程学院,哈尔滨150027

出　　处：《计算机应用》2018年第9期2455-2458,2463,共5页journal of Computer Applications

基　　金：国家自然科学基金面上项目(61672304);黑龙江省自然科学基金面上项目(F2015025);齐齐哈尔市科学技术工业攻关项目(GYGG-201620)~~

摘　　要：针对一类线性正则系统,传统迭代学习控制算法收敛速度较低的问题,设计了一种快速迭代学习控制算法。该算法在传统P型迭代学习控制算法基础上,增加了由相邻两次迭代时跟踪误差构成的上一次差分信号和当前差分信号,并在Lebesgue-p范数度量意义下,利用卷积推广的Young不等式严格证明了,当迭代次数趋于无穷大时,系统的跟踪误差收敛于零,并给出了算法的收敛条件。该算法与传统P型迭代学习控制算法相比,不仅提高了收敛速度,而且还避免了采用λ范数度量跟踪误差的缺陷,最后通过仿真结果进一步验证了所提算法的有效性。Focused on the problem that the convergence speed of traditional iterative learning control algorithm used in linear regular systems is slow,a kind of fast iterative learning control algorithm was designed for a class of linear regular systems.Compared with the traditional P-type iterative learning control algorithm,the algorithm increases tracking error at neighboring two iterations generated from last difference signal and present difference signal.And the convergence of the algorithm was proven by using Yong inequality of convolutional inference in the sense of Lebesgue-p norm.The results show the tracking error of the system will converge to zero with infinite iterations.The convergence condition is also given.Compared with P-type iterative learning control,the proposed algorithm can fasten the convergence and avoid the shortcomings of usingλnorm to measure the tracking error.Simulation further testifies the validity and effectiveness.

关 键 词：正则系统 迭代学习控制 Lebesgue-p范数 YOUNG不等式 跟踪误差 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]