A Structural Observation on Port-Hamiltonian Systems

Authors

Rainer H. Picard, Sascha Trostorff, Bruce Watson, Marcus Waurick

Abstract

We study port-Hamiltonian systems on a familiy of intervals and characterise all boundary conditions leading to $m$-accretive realisations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are based on a structural observation that the port-Hamiltonian operator can be transformed to the derivative on a familiy of reference intervals by suitable congruence relations allowing for studying the simpler case of a transport equation. Moreover, we provide well-posedness results for associated control problems without assuming any additional regularity of the operators involved.

Citation

• Journal: SIAM Journal on Control and Optimization
• Year: 2023
• Volume: 61
• Issue: 2
• Pages: 511–535
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/21m1441365

BibTeX

@article{Picard_2023,
  title={{A Structural Observation on Port-Hamiltonian Systems}},
  volume={61},
  ISSN={1095-7138},
  DOI={10.1137/21m1441365},
  number={2},
  journal={SIAM Journal on Control and Optimization},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Picard, Rainer H. and Trostorff, Sascha and Watson, Bruce and Waurick, Marcus},
  year={2023},
  pages={511--535}
}

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