Fluid dynamical systems as Hamiltonian boundary control systems

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

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    19 Citations (Scopus)
    71 Downloads (Pure)

    Abstract

    It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems, as recently obtained by the authors, can be adapted to formulate ideal adiabatic 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 previous publications 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
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2001

    Publication series

    NameMemorandum / Faculty of Mathematical Sciences
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1575
    ISSN (Print)0169-2690

    Keywords

    • MSC-35B37
    • MSC-35J55
    • MSC-70H05
    • IR-65762
    • MSC-93C20
    • MSC-58A10
    • EWI-3395
    • MSC-76N10

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