Authors

Arjan van der Schaft

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

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}
}

Download the bib file