Port-Hamiltonian Differential-Algebraic Systems

Authors

A. J. van der Schaft

Abstract

The basic starting point of port-Hamiltonian systems theory is network modeling ; considering the overall physical system as the interconnection of simple subsystems, mutually influencing each other via energy flow. As a result of the interconnections algebraic constraints between the state variables commonly arise. This leads to the description of the system by differential-algebraic equations (DAEs), i.e., a combination of ordinary differential equations with algebraic constraints. The basic point of view put forward in this survey paper is that the differential-algebraic equations that arise are not just arbitrary, but are endowed with a special mathematical structure; in particular with an underlying geometric structure known as a Dirac structure. It will be discussed how this knowledge can be exploited for analysis and control.

Keywords

Port-Hamiltonian systems; Passivity; Algebraic constraints; Kinematic constraints; Casimirs; Switching systems; Dirac structure; Interconnection; 34A09; 37J05; 70G45; 93B10; 93B27; 93C10

Citation

• ISBN: 9783642349270
• Publisher: Springer Berlin Heidelberg
• DOI: 10.1007/978-3-642-34928-7_5

BibTeX

@inbook{van_der_Schaft_2013,
  title={{Port-Hamiltonian Differential-Algebraic Systems}},
  ISBN={9783642349287},
  DOI={10.1007/978-3-642-34928-7_5},
  booktitle={{Surveys in Differential-Algebraic Equations I}},
  publisher={Springer Berlin Heidelberg},
  author={van der Schaft, A. J.},
  year={2013},
  pages={173--226}
}

Download the bib file

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