Port-Hamiltonian systems: an introductory survey

Arjan van der Schaft

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    101 Citations (Scopus)
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    Abstract

    The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models.
    Original languageUndefined
    Title of host publicationProceedings of the International Congress of Mathematicians Vol. III
    EditorsM. Sanz-Sole, J. Soria, J.L. Varona, J. Verdera
    Place of PublicationMadrid, Spain
    PublisherEuropean Mathematical Society Publishing House (EMS Ph)
    Pages1339-1365
    Number of pages27
    ISBN (Print)978-3-03719-022-7
    Publication statusPublished - 2006
    EventInternational Congress of Mathematicians - Madrid, Spain
    Duration: 22 Aug 200630 Aug 2006

    Publication series

    Name
    PublisherEuropean Mathematical Society Publishing House (EMS Ph)
    Numbersuppl 2

    Conference

    ConferenceInternational Congress of Mathematicians
    Period22/08/0630/08/06
    OtherAugust 22-30, 2006

    Keywords

    • MSC-70G45
    • MSC-70H05
    • MSC-70Q05
    • EWI-8632
    • METIS-237808
    • IR-66742
    • MSC-93A30

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