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Special Radon Semester on Computational Mechanics
Linz, October-December 2005
Abstract - Helmut Ennsbrunner and Kurt Schlacher

Authors: Helmut Ennsbrunner and Kurt Schlacher

Title of the contribution: Infinite dimensional port controlled Hamiltonian systems - geometric description and interconnection

Abstract:
Port controlled Hamiltonian systems with dissipation, or PCHD systems for short, have turned out to be a versatile tool for the mathematical modeling in control theory. This class of systems comes along with a mathematical description, that separates structural properties, storage elements and dissipative parts. Thus a network description of such plants, which is very useful for simulation and control, becomes available.
This contribution presents an extension of the PCH approach to the infinite dimensional case. It is shown, which differential geometric objects have to be introduced and how boundary conditions come into play. Additionally the key property of PCHD systems - their behavior with respect to interconnection - is investigated for domain and boundary interconnections. In the first part of the talk a short summary of the used mathematical notation is given. After that, some well known results for finite dimensional PCHD systems are presented. The third part is dedicated to the introduction of a possible extension of the approach to the infinite dimensional case. At first we confine ourselves to the case, where no differential operators are used. Here special attention is paid on the interconnection of two infinite dimensional PCHD systems via power conserving interconnections.
After that a formal definition of a differential operator is given and used to introduce a more general description of infinite dimensional PCHD systems.
Here we will not study the general case, but a very interesting application - the coupled field problem of elasticity, piezo electrics and the thermal field referred to as piezothermoelasticity.
Finally, a summary of the achieved results is given and remarks on extensions of the introduced approach close this contribution.

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