Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection

A. Macchelli, Alessandro Macchelli, Arjan van der Schaft, Claudio Melchiorri

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    19 Citations (Scopus)
    32 Downloads (Pure)

    Abstract

    In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.
    Original languageUndefined
    Title of host publicationProceedings of the 43rd IEEE Conference on Decision and Control
    Place of PublicationParadise Island, The Bahamas
    PublisherIEEE
    Pages3768-3773
    Number of pages6
    ISBN (Print)0-7803-8682-5
    Publication statusPublished - Dec 2004
    Event43rd IEEE Conference on Decision and Control, CDC 2004 - The Atlantis, Paradise Island, Bahamas
    Duration: 14 Dec 200417 Dec 2004
    Conference number: 43

    Publication series

    Name
    PublisherIEEE
    Volume4
    ISSN (Print)0191-2216

    Conference

    Conference43rd IEEE Conference on Decision and Control, CDC 2004
    Abbreviated titleCDC
    CountryBahamas
    CityParadise Island
    Period14/12/0417/12/04

    Keywords

    • IR-69161
    • METIS-220423
    • EWI-16814

    Cite this

    Macchelli, A., Macchelli, A., van der Schaft, A., & Melchiorri, C. (2004). Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. In Proceedings of the 43rd IEEE Conference on Decision and Control (pp. 3768-3773). Paradise Island, The Bahamas: IEEE.