A bilinear H2 model order reduction approach to linear parameter-varying systems

Peter Benner, X. Cao (Corresponding author), W.H.A. Schilders

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

This paper focuses on the model reduction problem for a special class of linear parameter-varying systems. This kind of systems can be reformulated as bilinear dynamical systems. Based on the bilinear system theory, we give a definition of the H2 norm in the generalized frequency domain. Then a model reduction method is proposed based on the gradient descent on the Grassmann manifold. The merit of the method is that by utilizing the gradient flow analysis, the algorithm is guaranteed to converge, and further speedup of the convergence rate can be achieved as well. Two numerical examples are tested to demonstrate the proposed method.
Language English Advances in Computational Mathematics 18 Apr 2019 10.1007/s10444-019-09695-9 E-pub ahead of print - 18 Apr 2019

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Linear Parameter-varying Systems
Bilinear Model
Model Order Reduction
Model Reduction
Grassmann Manifold
Bilinear Systems
System theory
Systems Theory
Reduction Method
Frequency Domain
Convergence Rate
Dynamical systems
Speedup
Dynamical system
Converge
Norm
Numerical Examples
Demonstrate

Keywords

• Bilinear dynamical systems
• Grassmann manifold
• Linear parameter-varying systems
• Model order reduction

Cite this

title = "A bilinear H2 model order reduction approach to linear parameter-varying systems",
abstract = "This paper focuses on the model reduction problem for a special class of linear parameter-varying systems. This kind of systems can be reformulated as bilinear dynamical systems. Based on the bilinear system theory, we give a definition of the H2 norm in the generalized frequency domain. Then a model reduction method is proposed based on the gradient descent on the Grassmann manifold. The merit of the method is that by utilizing the gradient flow analysis, the algorithm is guaranteed to converge, and further speedup of the convergence rate can be achieved as well. Two numerical examples are tested to demonstrate the proposed method.",
keywords = "Bilinear dynamical systems, Gradient descent, Grassmann manifold, Linear parameter-varying systems, Model order reduction",
author = "Peter Benner and X. Cao and W.H.A. Schilders",
year = "2019",
month = "4",
day = "18",
doi = "10.1007/s10444-019-09695-9",
language = "English",
journal = "Advances in Computational Mathematics",
issn = "1019-7168",
publisher = "Springer",

}

In: Advances in Computational Mathematics, 18.04.2019.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - A bilinear H2 model order reduction approach to linear parameter-varying systems

AU - Benner,Peter

AU - Cao,X.

AU - Schilders,W.H.A.

PY - 2019/4/18

Y1 - 2019/4/18

N2 - This paper focuses on the model reduction problem for a special class of linear parameter-varying systems. This kind of systems can be reformulated as bilinear dynamical systems. Based on the bilinear system theory, we give a definition of the H2 norm in the generalized frequency domain. Then a model reduction method is proposed based on the gradient descent on the Grassmann manifold. The merit of the method is that by utilizing the gradient flow analysis, the algorithm is guaranteed to converge, and further speedup of the convergence rate can be achieved as well. Two numerical examples are tested to demonstrate the proposed method.

AB - This paper focuses on the model reduction problem for a special class of linear parameter-varying systems. This kind of systems can be reformulated as bilinear dynamical systems. Based on the bilinear system theory, we give a definition of the H2 norm in the generalized frequency domain. Then a model reduction method is proposed based on the gradient descent on the Grassmann manifold. The merit of the method is that by utilizing the gradient flow analysis, the algorithm is guaranteed to converge, and further speedup of the convergence rate can be achieved as well. Two numerical examples are tested to demonstrate the proposed method.

KW - Bilinear dynamical systems

KW - Gradient descent

KW - Grassmann manifold

KW - Linear parameter-varying systems

KW - Model order reduction

UR - http://www.scopus.com/inward/record.url?scp=85064675856&partnerID=8YFLogxK

U2 - 10.1007/s10444-019-09695-9

DO - 10.1007/s10444-019-09695-9

M3 - Article

JO - Advances in Computational Mathematics

T2 - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

ER -