Einladung zum Vortrag im Kolloquium Technische Kybernetik

Hamiltonian formulation of network models of physical systems

Prof. Arjan van der Schaft

Institute of Mathematics and Computer Science
University of Groningen
Groningen, The Netherlands

    Zeit: Dienstag · 8. 11. 2005 · 16:00 Uhr
    Ort: Seminarraum 3.241 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

In this talk a framework for the modeling and control of complex physical systems is presented, which is based on a combination of the network and the Hamiltonian approach to physics. Historically, these two approaches have been developed separately from each other. While most of the analysis of physical systems has been performed within the Lagrangian and Hamiltonian framework, the network modeling point of view is revailing in the modeling and simulation of lumped-parameter complex physical systems.

We introduce a geometric model structure, called port-Hamiltonian systems, which encompasses both the standard Hamiltonian systems as encountered in analytical mechanics, as well as the network type models as arising e.g. in electrical, electro-mechanical and complex mechanical systems, and discuss its merits for analysis, simulation and control. Also, we indicate how the framework can be extended to (boundary controlled) distributed-parameter systems, and how this suggests the use of certain mixed-finite element methods for their approximation by finite-dimensional port-Hamiltonian systems.

Biographical Information

A.J.(Arjan) van der Schaft received the undergraduate and Ph.D. degrees in Mathematics from the University of Groningen, The Netherlands. In 1982 he joined the Department of Applied Mathematics, University of Twente, Enschede, The Netherlands; since 2000 as a full professor in Mathematical Systems and Control Theory. As of September 1, 2005, he has returned to the University of Groningen.

His research interests include issues of mathematical modeling in physics, engineering and systems biology, and the analysis and control of nonlinear and hybrid systems. He is the (co-)author of the following books: System Theoretic Descriptions of Physical Systems (1984), Variational and Hamiltonian Control Systems (1987, with P.E. Crouch) Nonlinear Dynamical Control Systems (1990, with H. Nijmeijer) L_2-Gain and Passivity Techniques in Nonlinear Control (second edition, 2000) An Introduction to Hybrid Dynamical Systems (2000, with J.M. Schumacher).