Surrogate-Based ℋ² Model Reduction of Port-Hamiltonian Systems

Authors

Tim Moser, Julius Durmann, Boris Lohmann

Abstract

Interpolatory methods for structure-preserving model reduction of port-Hamiltonian systems are especially suitable for very large-scale models, owing to their low computational cost and memory requirements. \( {[[:space:]]{\mathcal{H}[[:space:]]}_2} \)-based techniques iteratively search for models which fulfill a subset of first-order \( {[[:space:]]{\mathcal{H}[[:space:]]}_2} \)-optimality conditions. In each iteration, a new reduced-order model is computed, which might weaken the computational advantages in cases of slow convergence. We propose a new structure-preserving framework for port-Hamiltonian systems based on surrogate modeling. By exploiting the local nature of the \( {[[:space:]]{\mathcal{H}[[:space:]]}_2} \)-optimization problem, the cost of optimization is decoupled from the cost of reduction. Consequently, \( {[[:space:]]{\mathcal{H}[[:space:]]}_2} \)-based interpolatory methods can be accelerated significantly and especially for very large-scale port-Hamiltonian systems, which is illustrated by a numerical example.

Citation

• Journal: 2021 European Control Conference (ECC)
• Year: 2021
• Volume:
• Issue:
• Pages: 2058–2065
• Publisher: IEEE
• DOI: 10.23919/ecc54610.2021.9655109

BibTeX

@inproceedings{Moser_2021,
  title={{Surrogate-Based ℋ2 Model Reduction of Port-Hamiltonian Systems}},
  DOI={10.23919/ecc54610.2021.9655109},
  booktitle={{2021 European Control Conference (ECC)}},
  publisher={IEEE},
  author={Moser, Tim and Durmann, Julius and Lohmann, Boris},
  year={2021},
  pages={2058--2065}
}

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References

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