Port-Hamiltonian Systems on Simplicial Complexes
Geometric structures behind a variety of physical systems stemming from mechanics, electromagnetism and chemistry exhibit a remarkable unity enunciated by Dirac structures. The open dynamical systems defined with respect to these structures belong to the class of so-called port-Hamiltonian systems. These systems arise naturally from the energybased modeling. Apart from offering a geometric content of Hamiltonian systems, Dirac structures supply a framework for modeling port-Hamiltonian systems as interconnected and constrained systems. From a network-modeling perspective, this means that port-Hamiltonian systems can be reticulated into a set of energy-storing elements, a set of energy-dissipating elements, and a set of energy port by which the interconnection of these blocks and environment is modeled. It is well-known that such a modeling strategy also utilizes control synthesis for these systems. The port-Hamiltonian formalism transcends the lumpedparameter scenario and has been successfully applied to study of a number of distributed-parameter systems [1]. The centrepiece of the efforts concerning infinite-dimensional case is the Stokes-Dirac structure. The canonical StokesDirac structure is an infinite-dimensional Dirac structure de- fined in terms of differential forms on a smooth manifold with boundary. The Hamiltonian equations associated to this Dirac structure.