K-power双线性系统基于Laguerre函数的保结构模型降阶方法  

Structure Preserving Model Order Reduction for K-power Bilinear Systems Based on Laguerre Functions

作　　者：金辉 肖志华 祁振中 JIN Hui;XIAO Zhihua;QI Zhenzhong(School of Information and Mathematics,Yangtze University,Jingzhou 434023,China;School of Mathematics,Northwest University,Xi’an 710127,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023 [2]西北大学数学学院,陕西西安710127

出　　处：《应用数学》2023年第4期929-939,共11页Mathematica Applicata

基　　金：国家自然科学基金项目(62273059,61803046)。

摘　　要：针对K-power双线性系统,提出一种基于Laguerre函数的保结构模型降阶方法.该方法首先将K-power双线性系统转化为一般的双线性系统,再利用矩阵指数函数的Laguerre函数展开,计算出双线性系统交叉Gram矩阵的近似低秩因子,从而构造K-power双线性系统各子系统相应的投影变换,进而生成该系统的近似平衡系统.然后,通过截断较小的奇异值对应的状态,得到降阶模型.该降阶过程计算高效,且具有一定的自适应性.最后,数值实验验证了算法的有效性.A structure preserving model order reduction method for K-power bilinear systems based on Laguerre functions is proposed.Firstly,the method aims to transform the K-power bilinear system into a general bilinear system and calculate the approximate low-rank factors of the cross Gramian of the bilinear system by Laguerre functions expansion of the matrix exponential function.After that,the approximate balanced system of the K-power bilinear system is constructed by the corresponding projection transformation of each subsystem.Then,the reduced order model is obtained by truncating the states corresponding to smaller singular values.The process of model order reduction is flexible,efficient and adaptive.Finally,a numerical experiment is given to demonstrate the effectiveness of the algorithm.

关 键 词：模型降阶 K-power双线性系统 LAGUERRE函数 交叉Gram矩阵 

分 类 号：O231.2[理学—运筹学与控制论]