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.
LanguageEnglish
JournalAdvances in Computational Mathematics
Early online date18 Apr 2019
DOIs
StateE-pub ahead of print - 18 Apr 2019

Fingerprint

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

Keywords

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

Cite this

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A bilinear H2 model order reduction approach to linear parameter-varying systems. / Benner, Peter; Cao, X. (Corresponding author); Schilders, W.H.A.

In: Advances in Computational Mathematics, 18.04.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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