Port-Hamiltonian systems on discrete manifolds

Authors

Marko Šešlija, Jacquelien M.A. Scherpen, Arjan van der Schaft

Abstract

This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finite-dimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of finite-dimensional port-Hamiltonian systems that emulate the behaviour of the open distributed-parameter systems with Hamiltonian dynamics.

Keywords

Port-Hamiltonian systems; Dirac structures; distributed-parameter systems; structure-preserving discretization; discrete geometry

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2012
• Volume: 45
• Issue: 2
• Pages: 774–779
• Publisher: Elsevier BV
• DOI: 10.3182/20120215-3-at-3016.00137
• Note: 7th Vienna International Conference on Mathematical Modelling

BibTeX

@article{_e_lija_2012,
  title={{Port-Hamiltonian systems on discrete manifolds}},
  volume={45},
  ISSN={1474-6670},
  DOI={10.3182/20120215-3-at-3016.00137},
  number={2},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Šešlija, Marko and Scherpen, Jacquelien M.A. and van der Schaft, Arjan},
  year={2012},
  pages={774--779}
}

Download the bib file

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