On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems

We consider infinite-dimensional port-Hamiltonian systems with respect to control issues. In contrast to the well-established representation relying on Stokes-Dirac structures that are based on skew-adjoint differential operators and the use of energy variables, we employ a different port-Hamiltonian framework. Based on this system representation conditions for Casimir functionals will be derived where in this context the variational derivative plays an extraordinary role. Furthermore the coupling of finite- and infinite-dimensional systems will be analyzed in the spirit of the control by interconnection problem.