Motivated from modeling modern energy transport networks, in particular those from different physical domains, the modeling framework of port-Hamiltonian systems is discussed. The classical port-Hamiltonian approach is systematically extended to constrained dynamical systems (partial-differential-algebraic equations). A new algebraically and geometrically defined system structure is derived, which has many nice mathematical properties. It is shown that this structure is invariant under Galerkin projections, changes of basis, and that a dissipation inequality holds. If such a system is controllable and observable then it is automatically stable and passive. Furthermore, the new representation is very robust to perturbations in the system structure.
There exist, however, many open problems associated with port -Hamiltonian systems. These include the adequate choice of time-integration methods that guarantee the dissipation inequality, the generation of such systems from pure input-output data, as well as good model reduction and optimal control techniques that make optimal use of the structure.|