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Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems

  • A. J. van der Schaft
Part of the International Centre for Mechanical Sciences book series (CISM, volume 444)

Abstract

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamiltonian function given by the total stored energy. The structural properties of port-Hamiltonian systems are discussed, in particular the existence of Casimir functions and its implications for stability and stabilization. Furthermore it is shown how passivity-based control results from interconnecting the plant port-Hamiltonian system with a controller port-Hamiltonian system, leading to a closed-loop port-Hamiltonian system. Finally, extensions to the distributed-parameter case are provided by formulating boundary control systems as infinite-dimensional port-Hamiltonian systems.

Keywords

Hamiltonian System Multibody System Kinematic Constraint Dirac Structure Bond Graph 
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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • A. J. van der Schaft
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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