Port-Hamiltonian systems: an introductory survey
Authors
Abstract
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models.
Citation
- ISBN: 9783985470389
- Publisher: EMS Press
- DOI: 10.4171/022-3/65
BibTeX
@inbook{van_der_Schaft_2007,
title={{Port-Hamiltonian systems: an introductory survey}},
ISBN={9783985475384},
DOI={10.4171/022-3/65},
booktitle={{Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006}},
publisher={EMS Press},
author={van der Schaft, Arjan},
year={2007},
pages={1339--1365}
}