Optimization-based model order reduction of port-Hamiltonian descriptor systems

Authors

Paul Schwerdtner, Tim Moser, Volker Mehrmann, Matthias Voigt

Abstract

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian differential–algebraic equations (pH-DAEs). Our method is based on a novel parameterization that allows us to represent any linear time-invariant pH-DAE of a prescribed model order. We propose two algorithms which directly optimize the parameters of a reduced model to approximate a given large-scale model with respect to either the H ∞ or the H 2 norm. This approach has several benefits. Our parameterization ensures that the reduced model is again a pH-DAE system and enables a compact representation of the algebraic part of the large-scale model, which in projection-based methods often requires a more involved treatment. The direct optimization is entirely based on transfer function evaluations of the large-scale model and is therefore independent of the structure of the system matrices. Numerical experiments are conducted to illustrate the high accuracy and small reduced model orders in comparison to other structure-preserving MOR methods.

Keywords

descriptor systems, model order reduction, port-hamiltonian systems, structure-preservation

Citation

Journal: Systems & Control Letters
Year: 2023
Volume: 182
Issue:
Pages: 105655
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2023.105655

BibTeX

@article{Schwerdtner_2023,
  title={{Optimization-based model order reduction of port-Hamiltonian descriptor systems}},
  volume={182},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2023.105655},
  journal={Systems \&amp; Control Letters},
  publisher={Elsevier BV},
  author={Schwerdtner, Paul and Moser, Tim and Mehrmann, Volker and Voigt, Matthias},
  year={2023},
  pages={105655}
}

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