Structure-preserving H∞ control for port-Hamiltonian systems

Authors

Tobias Breiten, Attila Karsai

Abstract

We study H ∞ control design for linear time-invariant port-Hamiltonian systems. By a modification of the two central algebraic Riccati equations, we ensure that the resulting controller will be port-Hamiltonian. Using these modified equations, we proceed to show that a corresponding balanced truncation approach preserves port-Hamiltonian structure. We illustrate the theoretical findings using numerical examples and observe that the chosen representation of the port-Hamiltonian system can have an influence on the approximation qualities of the reduced order model.

Citation

• Journal: Systems & Control Letters
• Year: 2023
• Volume: 174
• Issue:
• Pages: 105493
• Publisher: Elsevier BV
• DOI: 10.1016/j.sysconle.2023.105493

BibTeX

@article{Breiten_2023,
  title={{Structure-preserving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e277" altimg="si741.svg"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control for port-Hamiltonian systems}},
  volume={174},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2023.105493},
  journal={Systems &amp; Control Letters},
  publisher={Elsevier BV},
  author={Breiten, Tobias and Karsai, Attila},
  year={2023},
  pages={105493}
}

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