Port Hamiltonian Formulation of Innite Dimensional Systems I. Modeling

Abstract In this paper, some new results concerning the modeling of distributed parameter systems in port Hamilto-nian form are presented. The classical nite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case. The resulting class of innite dimensional sys-tems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of nite dimensional Dirac structure in order to deal with an innite dimensional space of power variables. In this way, also in the distributed parameter case, the variation of total energy within the spatial domain of the system can be related to the power ow through the boundary. Since this relation deeply relies on the Stokes theorem, these structures are called StokesDirac structures I