Frequency-Interval Model Reduction of Bilinear Systems

被引：37

作者：

Shaker, Hamid Reza ^{[1
]}

Tahavori, Maryamsadat ^{[2
,3
]}

机构：

[1] Aalesund Univ Coll, Fac Engn & Nat Sci, NO-6025 Alesund, Norway

[2] Aalborg Univ, Dept Elect Syst, DK-9220 Aalborg, Denmark

[3] Univ London Imperial Coll Sci Technol & Med, Dept Elect & Elect Engn, London, England

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2014年 / 59卷 / 07期

关键词：

Bilinear systems; frequency-interval; generalized Lyapunov equation; gramians; model reduction; WEIGHTED BALANCED TRUNCATION; ORDER REDUCTION; TIME;

D O I：

10.1109/TAC.2013.2295661

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this technical note, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.

引用

页码：1948 / 1953

页数：6

共 25 条

[1] NEW MODEL-REDUCTION SCHEME FOR BILINEAR-SYSTEMS
ALBAIYAT, SA
BETTAYEB, M
ALSAGGAF, UM
[J]. INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1994, 25 (10) : 1631 - 1642
[2] [Anonymous], 1991, Applications to Bilinear Control
[3] ANTOULAS A. C., 2005, ADV DES CONTROL, DOI 10.1137/1.9780898718713
[4] Model Reduction by Moment Matching for Linear and Nonlinear Systems
Astolfi, Alessandro
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (10) : 2321 - 2336
[5] LYAPUNOV EQUATIONS, ENERGY FUNCTIONALS, AND MODEL ORDER REDUCTION OF BILINEAR AND STOCHASTIC SYSTEMS
Benner, Peter
Damm, Tobias
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (02) : 686 - 711
[6] REALIZATION AND STRUCTURE THEORY OF BILINEAR DYNAMICAL-SYSTEMS
DALESSANDRO, P
ISIDORI, A
RUBERTI, A
[J]. SIAM JOURNAL ON CONTROL, 1974, 12 (03): : 517 - 535
[7] CANONICAL-FORMS FOR BILINEAR-SYSTEMS
DORISSEN, HT
[J]. SYSTEMS & CONTROL LETTERS, 1989, 13 (02) : 153 - 160
[8] Dullerud G.E., 2000, A Course in Robust Control Theory: A Convex Approach, VVolume 6
[9] Weighted balanced truncation for unstable nonlinear systems using coprime factorizations
Fujimoto, Kenji
Mizuno, Hikaru
[J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 3843 - 3848
[10] MODEL-REDUCTION IN LIMITED TIME AND FREQUENCY INTERVALS
GAWRONSKI, W
JUANG, JN
[J]. INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1990, 21 (02) : 349 - 376

← 1 2 3 →