Fluid dynamical systems as Hamiltonian boundary control systems

A.J. van der Schaft, B.M. Maschke

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    Abstract

    It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems as recently provided in [11, 12] can be adapted to formulate ideal isentropic compressible fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure introduced in [11] to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.
    Original languageEnglish
    Title of host publicationProceedings of the 40th IEEE Conference on Decision and Control, CDC 2001
    Place of PublicationLos Alamitos, CA
    PublisherIEEE
    Pages4497-4502
    Number of pages6
    ISBN (Print)0-7803-7061-9
    DOIs
    Publication statusPublished - 2001
    Event40th IEEE Conference on Decision and Control, CDC 2001 - Hyatt Regency Grand Cypress, Orlando, United States
    Duration: 4 Dec 20017 Dec 2001

    Conference

    Conference40th IEEE Conference on Decision and Control, CDC 2001
    Abbreviated titleCDC
    Country/TerritoryUnited States
    CityOrlando
    Period4/12/017/12/01

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