阻尼陀螺系统的输出反馈控制修正方法  

A METHOD FOR UPDATING DAMPED GYROSCOPIC SYSTEMS BY USING OUTPUT FEEDBACK CONTROL

作　　者：丁莹莹 刘皞 Ding Yingying;Liu Hao(Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106)

机构地区：[1]南京航空航天大学数学系,南京211106 [2]飞行器数学建模与高性能计算工业和信息化部重点实验室(南京航空航天大学),南京211106

出　　处：《高等学校计算数学学报》2022年第3期230-242,共13页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11401305);中央高校基本科研业务费专项资金资助(NS2020053)。

摘　　要：1引言考虑以下阻尼陀螺控制系统M_(a)q(t)+(G_(a)+D_(a))q(t)+K_(a)q(t)=Bu(t),(1)其中M_(a),G_(a),D_(a),K_(a)∈R^(n×n)分别为质量矩阵、陀螺矩阵、阻尼矩阵以及刚度矩阵,Ma为对称正定矩阵,Ga为反对称矩阵,Da为对称矩阵,Ka为对称半正定矩阵,且B∈Rn×m为列满秩控制矩阵,u(t)∈R~m为控制向量.This paper concerns the matrix model updating problem of damped gyroscopic systems.In order to ensure the stability of damped gyroscopic systems,a modified conjugate gradient method is proposed to update the mass,damping,gyroscopic and stiffness matrix simultaneously by using output feedback,and the optimal approximation solution in the sense of Frobenius norm is obtained.Numerical examples show that the proposed method is effective.

关 键 词：对称正定矩阵 反对称矩阵 质量矩阵 对称半正定矩阵 列满秩 输出反馈控制 阻尼矩阵 刚度矩阵 

分 类 号：O241.6[理学—计算数学]