On composition of Dirac structures and its implications for control by interconnection

Joaquin Cervera, Arjan van der Schaft, Alfonso Baños

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    Abstract

    Network modeling of complex physical systems leads to a class of nonlinear systems, called Port-Controlled Hamiltonian Systems (PCH systems). These systems are geometrically defined by a state space manifold of energy variables, a power-conserving interconnection formalized as a Dirac structure, together with the total stored energy and a resistive structure. Basic features of these systems include their compositionality properties (a power-conserving interconnection of PCH systems is again a PCH system), and their stability and stabilizability properties exploiting the energy function and the Casimir functions. In the present paper we further elaborate on the compositionality properties of Dirac structures by providing an explicit parametrization of all achievable closed-loop Dirac structures in terms of their constituent parts. Amongst others this opens up the way to a complete characterization of the class of PCH systems which are stabilizable by interconnection with a PCH controller.
    Original languageUndefined
    Title of host publicationNonlinear and Adaptive Control
    EditorsAlan Zinober, David Owens
    Place of PublicationBerlin
    PublisherSpringer
    Pages55-63
    Number of pages9
    ISBN (Print)978-3-540-43240-1
    DOIs
    Publication statusPublished - 2003

    Publication series

    NameLecture Notes in Control and Information Sciences
    PublisherSpringer Verlag
    Number281
    Volume281
    ISSN (Print)0170-8643

    Keywords

    • EWI-16770
    • METIS-211065
    • IR-69148

    Cite this

    Cervera, J., van der Schaft, A., & Baños, A. (2003). On composition of Dirac structures and its implications for control by interconnection. In A. Zinober, & D. Owens (Eds.), Nonlinear and Adaptive Control (pp. 55-63). [10.1007/3-540-45802-6_5] (Lecture Notes in Control and Information Sciences; Vol. 281, No. 281). Berlin: Springer. https://doi.org/10.1007/3-540-45802-6_5