Model Reduction for Parametric Systems Using Balanced Truncation and Interpolation

被引：47

作者：

Baur, Ulrike ^{[1
]}

Benner, Peter ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

AT-AUTOMATISIERUNGSTECHNIK | 2009年 / 57卷 / 08期

关键词：

Parametric model order reduction; balanced truncation; interpolation; sparse grids;

D O I：

10.1524/auto.2009.0787

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 presents a parameter-preserving approach for model order reduction of parameterized, linear systems. The proposed method is a coupling of balanced truncation with interpolation. Thus, error estimates for the quality of the reduced-order system can be derived. The method can be applied to systems containing several parameters by using sparse grids for the discretization of the parameter space.

引用

页码：411 / 419

页数：9

共 32 条

[11]

Farle O., 2006, Automatisierungstechnik, V54, P161, DOI 10.1524/auto.2006.54.4.161

[12] Parameter independent model order reduction [J].

Feng, LH .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2005, 68 (03) :221-234

[13] ALL OPTIMAL HANKEL-NORM APPROXIMATIONS OF LINEAR-MULTIVARIABLE SYSTEMS AND THEIR L INFINITY-ERROR BOUNDS [J].

GLOVER, K .

INTERNATIONAL JOURNAL OF CONTROL, 1984, 39 (06) :1115-1193

[14]

GRIEBEL M, 1991, NOTE NUM FL, V31, P94

[15] H2 MODEL REDUCTION FOR LARGE-SCALE LINEAR DYNAMICAL SYSTEMS [J].

Gugercin, S. ;

Antoulas, A. C. ;

Beattie, C. .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (02) :609-638

[16] A modified low-rank Smith method for large-scale Lyapunov equations [J].

Gugercin, S ;

Sorensen, DC ;

Antoulas, AC .

NUMERICAL ALGORITHMS, 2003, 32 (01) :27-55

[17]

Gugercin S., 2005, LECT NOTES COMPUTATI, V45, P49

[18]

HANKEBOURGEOIS M, 2006, GRUNDLAGEN NUMERISCH

[19] KRYLOV SUBSPACE METHODS FOR SOLVING LARGE LYAPUNOV EQUATIONS [J].

JAIMOUKHA, IM ;

KASENALLY, EM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (01) :227-251

[20] Algorithm 847: spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB [J].

Klimke, A ;

Wohlmuth, B .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2005, 31 (04) :561-579

← 1 2 3 4 →