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

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

doi:10.1109/CDC.2010.5717698

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

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

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 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 language	English
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6265-6270
Number of pages	6
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5717698
Publication status	Published - 2010
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: 2010 Dec 15 → 2010 Dec 17

Publication series

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

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	10/12/15 → 10/12/17

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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10.1109/CDC.2010.5717698

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Vankerschaver, J., Yoshimura, H., Leok, M., & Marsden, J. E. (2010). Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 6265-6270). [5717698] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2010.5717698

Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. / Vankerschaver, Joris; Yoshimura, Hiroaki; Leok, Melvin et al.

2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 6265-6270 5717698 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Vankerschaver, J, Yoshimura, H, Leok, M & Marsden, JE 2010, Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717698, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6265-6270, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 10/12/15. https://doi.org/10.1109/CDC.2010.5717698

Vankerschaver J, Yoshimura H, Leok M, Marsden JE. Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc. 2010. p. 6265-6270. 5717698. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2010.5717698

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

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