一类扰动线性方程组的迭代学习控制求解方法  

Iterative learning control method for solving a class of perturbed linear algebraic equations

作　　者：李钧涛[1] 梁聪 汤永 Li Juntao;Liang Cong;Tang Yong(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China;Xinxiang Aviation Industry(Group)Co.,Ltd,Xinxiang 453003,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]新乡航空工业(集团)有限公司,河南新乡453003

出　　处：《河南师范大学学报（自然科学版）》2022年第6期8-14,F0002,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(61203293);河南省科技攻关计划(212102210140).

摘　　要：针对一类系数矩阵中含有扰动的线性方程组,提出了一种基于迭代学习控制的求解方法.首先将扰动线性方程组的求解问题转化为线性离散不确定系统的可镇定性问题;接着给出了扰动线性方程组有解的一个充分条件.然后,通过Lyapunov函数设计状态反馈控制器,得到确定迭代学习控制系统的学习律,并获得不确定系统跟踪误差的上界及扰动线性方程组的近似解.最后仿真实验验证了所提求解方法的有效性.A solving method based on iterative learning control was proposed for a class of linear algebraic equations with perturbations in the coefficient matrix.Firstly,the solving of linear algebraic equations with perturbations was transformed to study the stabilizability of a linear discrete uncertain system;then,a sufficient condition for the solvability of the perturbed linear algebraic equations was given.After that,the state feedback controller was designed by the Lyapunov function to obtain the learning law of the deterministic iterative learning control system,based on which the upper bound of the tracking error of the uncertain system and the approximate solution of the perturbed linear algebraic equations were obtained.Finally,the simulation experiments verified the effectiveness of the proposed method.

关 键 词：扰动线性方程组 迭代学习 状态反馈 

分 类 号：TP271.8[自动化与计算机技术—检测技术与自动化装置]