Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures

Joris Vankerschaver*, Hiroaki Yoshimura, Melvin Leok, Jerrold E. Marsden

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, we recover not only the standard structure matrix of Stokes-Dirac structures, but also the typical non-canonical advection terms in (for instance) the Euler equation.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6265-6270
Number of pages6
ISBN (Print)9781424477456
DOIs
Publication statusPublished - 2010
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: 2010 Dec 152010 Dec 17

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States
CityAtlanta
Period10/12/1510/12/17

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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