TY - GEN
T1 - Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures
AU - Vankerschaver, Joris
AU - Yoshimura, Hiroaki
AU - Leok, Melvin
AU - Marsden, Jerrold E.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC.2010.5717698
DO - 10.1109/CDC.2010.5717698
M3 - Conference contribution
AN - SCOPUS:79953155280
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6265
EP - 6270
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -