Fluid dynamical systems as Hamiltonian boundary control systems

It is shown how the geometric framework for distributed-parameter portcontrolled Hamiltonian systems as recently provided in [14, 15] can be adapted to formulate ideal adiabatic fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure introduced in [14] to a Dirac structure defined on the space of mass density 3-forms and velocity 1forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.