K-power系统在Grassmann流形上的单侧模型降阶方法  

ONE-SIDE MODEL REDUCTION OF K-POWER SYSTEMS ON THE GRASSMANN MANIFOLD

作　　者：杨平[1] 徐康丽[1] 蒋耀林[1,2] 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046 [2]西安交通大学数学与统计学院,西安710049

出　　处：《数值计算与计算机应用》2016年第1期41-56,共16页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11371287)

摘　　要：K-power系统作为一类比较特殊的双线性系统,可以由一系列阶数相对较小的子系统构成,这使得K-power系统具有特殊的结构.K-power系统在Grassmann流形上的模型降阶方法将误差系统的H_2范数看作是定义在Grassmann流形上的代价函数,然后,沿测地线执行线性搜索寻找使得代价函数最小的变换矩阵.为了保持系统降阶前后结构的一致性,算法以K-power系统中各个子系统的变换矩阵为对角线元素构成双线性系统的变换矩阵.此外,算法有效地利用了K-power系统的结构特性,使得该算法在对K-power系统进行降阶时较一般的双线性系统的模型降阶方法有更少的计算量.The K-power system is regarded as a kind of special bilinear systems, which can be made up of some lower order subsystems. This allows the K-power system to have the special structure. The /-/2 norm of the error system is seen as the cost function defined on the Grassmann manifold. Fhrther, we operate the linear search along the negative gradient to seek the transformation matrix to make the cost function the smallest. In order to retain the structure of the reduced system in accordance with that of the original system, the transformation matrix of the bilinear system is the block diagonal matrix, whose diagonal blocks consist of the transformation matrices of the subsystems in the K-power system in the corresponding algorithm. In addition, By making full use of the structure of the K- power system, the algorithm costs less computational quantity than the other bilinear model reduction methods for reducing the order of the K-power system.

关 键 词：模型降阶 K—power系统 H2最优 GRASSMANN流形 代价函数. 

分 类 号：O186.12[理学—数学]