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

Authors

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

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.

Citation

• Journal: 49th IEEE Conference on Decision and Control (CDC)
• Year: 2010
• Volume:
• Issue:
• Pages: 6265–6270
• Publisher: IEEE
• DOI: 10.1109/cdc.2010.5717698

BibTeX

@inproceedings{Vankerschaver_2010,
  title={{Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures}},
  DOI={10.1109/cdc.2010.5717698},
  booktitle={{49th IEEE Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Vankerschaver, Joris and Yoshimura, Hiroaki and Leok, Melvin and Marsden, Jerrold E.},
  year={2010},
  pages={6265--6270}
}

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References

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