A trust-region method for H2 model reduction of bilinear systems on the Stiefel manifold

被引：14

作者：

Yang, Ping ^{[1
]}

Jiang, Yao-Lin ^{[1
,2
]}

Xu, Kang-Li ^{[2
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2019年 / 356卷 / 04期

关键词：

Model reduction; Bilinear systems; Riemannian trust-region method; H-2-optimality; GENERAL ORTHOGONAL POLYNOMIALS; ORDER REDUCTION; GEOMETRY;

D O I：

10.1016/j.jfranklin.2019.01.024

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper investigates the Riemannian trust-region method for H-2 model reduction of bilinear systems. The H-2 error norm is treated as a cost function on the Stiefel manifold such that the orthogonality constraint for the projection matrix is plainly satisfied. The property related to the Euclidean gradient is studied. Then, the inner product associated with the Riemannian Hessian is derived, which can simplify the expression of the trust-region subproblem. The trust-region method for H-2 model reduction is accordingly established and the convergence is further discussed. Finally, two numerical examples are employed to demonstrate the performance of the proposed method. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：2258 / 2273

页数：16

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