Infinite-Dimensional Port-Hamiltonian Systems

This chapter presents the formulation of distributed parameter systems in terms of port-Hamiltonian system. In the first part it is shown, for different examples of physical systems defined on one-dimensional spatial domains, how the Dirac structure and the port-Hamiltonian formulation arise from the description of distributed parameter systems as systems of conservation laws. In the second part we consider systems of two conservation laws, describing two physical domains in reversible interaction, and it is shown that they may be formulated as port-Hamiltonian systems defined on a canonical Dirac structure called canonical Stokes-Dirac structure. In the third part, this canonical Stokes-Dirac structure is generalized for the examples of the Timoshenko beam, a nonlinear flexible link, and the ideal compressible fluid in order to encompass geometrically complex configurations and the convection of momentum.