A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

Authors

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

Abstract

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate that they provide a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. This approach of discrete differential geometry, rather than discretizing the partial differential equations, allows to first discretize the underlying Stokes-Dirac structure and then to impose the corresponding finite-dimensional port-Hamiltonian dynamics. In this manner, we preserve a number of important topological and geometrical properties of the system.

Citation

• Journal: IEEE Conference on Decision and Control and European Control Conference
• Year: 2011
• Volume:
• Issue:
• Pages: 7003–7008
• Publisher: IEEE
• DOI: 10.1109/cdc.2011.6160579

BibTeX

@inproceedings{Seslija_2011,
  title={{A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems}},
  DOI={10.1109/cdc.2011.6160579},
  booktitle={{IEEE Conference on Decision and Control and European Control Conference}},
  publisher={IEEE},
  author={Seslija, Marko and Scherpen, Jacquelien M.A. and van der Schaft, Arjan},
  year={2011},
  pages={7003--7008}
}

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