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

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.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok, Jerrold E. Marsden
• Keywords: Canonical Dirac Structure, CDC 2010, Control Systems, Stokes-Dirac Structures, Typical Non-canonical Advection