Topological Geometry and Control for Distributed Port-Hamiltonian Systems with Non-Integrable Structures

This paper discusses topological geometrical aspects and a control strategy for a distributed port-Hamiltonian system with a non-integrable structure called a distributed energy structure. First, we show a geometrical structure of port variables determined by differential forms. Next, we state the necessary condition for regarding the distributed energy structure as a boundary energy structure which is boundary integrable. From these results, we define the fundamental form that generates the distributed port-Hamiltonian system with distributed energy structures in a variational problem. Finally, we present a new concept of boundary controls for the distributed port-Hamiltonian system with distributed energy structures in space-time coordinates.