Moving-Boundary Port-Hamiltonian Systems

Abstract: In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally introduce a new class of moving-boundary port-Hamiltonian systems by showing that these distributed parameter systems on a time-varying spatial domain admit a port-Hamiltonian representation. We demonstrate that our results can be leveraged to develop a spatial discretization scheme with dynamic meshing for approximating the telegrapher's equations on a time-varying spatial domain, which we subsequently verify numerically.