Hamiltonian discretization of boundary control systems

G. Golo, V. Talasila, Arjan van der Schaft, B.M. Maschke

    Research output: Contribution to journalArticleAcademicpeer-review

    106 Citations (Scopus)

    Abstract

    A fundamental problem in the simulation and control of complex physical systems containing distributed-parameter components concerns finite-dimensional approximation. Numerical methods for partial differential equations (PDEs) usually assume the boundary conditions to be given, while more often than not the interaction of the distributed-parameter components with the other components takes place precisely via the boundary. On the other hand, finite-dimensional approximation methods for infinite-dimensional input–output systems (e.g., in semi-group format) are not easily relatable to numerical techniques for solving PDEs, and are mainly confined to linear PDEs. In this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements, resulting in a finite-dimensional input–output system. The approach is based on formulating the distributed-parameter component as an infinite-dimensional port-Hamiltonian system, and exploiting the geometric structure of this representation for the choice of appropriate mixed finite elements. The spatially discretized system is again a port-Hamiltonian system, which can be treated as an approximating lumped-parameter physical system of the same type. In the current paper this program is carried out for the case of an ideal transmission line described by the telegrapher's equations, and for the two-dimensional wave equation.
    Original languageUndefined
    Article number10.1016/j.automatica.2003.12.017
    Pages (from-to)757-771
    Number of pages15
    JournalAutomatica
    Volume40
    Issue number5
    DOIs
    Publication statusPublished - May 2004

    Keywords

    • Boundary control
    • Finite elements
    • Spatial discretization
    • IR-69097
    • EWI-16796
    • METIS-219848
    • Port Hamiltonian Systems

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