具有反馈信息的迭代学习控制律在Lebesgue-p范数意义下的收敛性  

Convergence of Iterative Learning Control with Feedback Information in the Sense of Lebesgue-p Norm

作　　者：阮小娥[1] 连建帮[1] 吴慧卓[1] 

机构地区：[1]西安交通大学理学院数学系,西安710049

出　　处：《自动化学报》2011年第4期513-516,共4页Acta Automatica Sinica

基　　金：国家自然科学基金(F030114-60974140)资助~~

摘　　要：针对一类线性时不变系统,提出了具有反馈信息的PD-型(Proportional-derivative-type)迭代学习控制律,利用卷积的推广的Young不等式,分析了控制律在Lebesgue-p范数意义下的单调收敛性.分析表明,收敛性不但决定于系统的输入输出矩阵和控制律的微分学习增益,而且依赖于系统的状态矩阵和控制律的比例学习增益;进一步,当适当选取反馈增益时,反馈信息可加快典型的PD-型迭代学习控制律的单调收敛性.数值仿真验证了理论分析的正确性和控制律的有效性.This paper addresses a kind of proportional-derivative-type（PD-type）iterative learning control updating law with feedback information for a class of linear time-invariant systems.By taking advantage of the generalized Young inequality of convolution integral,monotone convergence of the updating law is analyzed in the sense of Lebesgue-p norm.The analysis indicates that the convergence is determined not only by the system input-output matrix and the derivative learning gain,but also by the system state matrix and the proportional learning gain.It is further shown that the feedback information may speed up the convergence of the typical PD-type rule when the feedback gains are properly chosen.Numerical simulation exhibits the validity and the effectiveness.

关 键 词：迭代学习控制 反馈 Lebesgue-p范数 单调收敛 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]