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

Seslija, M., Scherpen, J. M. A. & van der Schaft, A., 2011, Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). NEW YORK: University of Groningen, Research Institute of Technology and Management, p. 7003-7008 6 p.

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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.
Original languageEnglish
Title of host publicationProceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
Place of PublicationNEW YORK
PublisherUniversity of Groningen, Research Institute of Technology and Management
Pages7003-7008
Number of pages6
ISBN (Electronic)9781612847993
ISBN (Print)9781612848006
Publication statusPublished - 2011
Event50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) -
Duration: 12-Dec-201115-Dec-2011

Other

Other50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC)
Period12/12/201115/12/2011

Event

50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC)

12/12/201115/12/2011

Event: Other

    Keywords

  • MULTISYMPLECTIC GEOMETRY, VARIATIONAL INTEGRATORS

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