线性广义系统P型迭代学习控制在L^p范数意义下的收敛性  

Convergence of P type Iterative Learning Control for a Class of Linear Generalized System in the Sense of L^p Norm

作　　者：张克军[1] 刘芳[1] 刘万利 ZHANG Ke-jun;LIU Fang;LIU Wan-li(School of Math and Physical Sciences,Xuzhou Institute of Technology,Xuzhou 221018,China)

机构地区：[1]徐州工程学院数理学院,徐州221018

出　　处：《科学技术与工程》2020年第7期2773-2777,共5页Science Technology and Engineering

基　　金：江苏省自然科学基金(BK20170248);徐州市科技项目(KC18013);徐州工程学院培育项目(XKY2017112)。

摘　　要：在对一类线性广义系统进行非奇异变换后,利用卷积的推广Young不等式,在Lebesgue-p(L^p)范数意义下,研究了一、二阶P型迭代学习控制算法的收敛条件,并对两种算法的收敛速度进行了比较。理论分析表明,控制算法的收敛条件、收敛速度与学习增益矩阵、系统本身属性有关;如果选取合适的学习增益矩阵,则二阶P型控制算法的收敛速度快于一阶的。仿真实验验证了控制算法的可行性和理论的正确性。After nonsingular transformation for a class of linear generalized system,by taking advantage of the generalized Young inequality of convolution integral,the convergence conditions of first and second-order P type iterative learning control were studied in the sense of Lebesgue-p(L^p)norm,and the convergence speeds of both of control algorithms were compared.Results manifest that,the convergence condition and speed are related to the learning gain matrices and the attributes of the system itself,and the second-order P-type control algorithm has faster convergence speed than the first-order under some given Proper learning gain matrices.The simulations support the feasibility of these control algorithms and the correctness of the theory.

关 键 词：迭代学习控制 广义系统 L^p范数 收敛性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]