Fluid dynamical systems as Hamiltonian boundary control systems

It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems, as recently obtained by the authors, 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 previous publications to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, 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.