Port-Hamiltonian systems: a theory for modeling, simulation and control of complex physical systems

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. The structural properties of these systems are discussed, in particular the existence of Casimir functions and their implications for stabilty. It is shown how a power-conserving interconnection of port-Hamiltonian systems defines another port-Hamiltonian system, and how this may be used for control by shaping the internal energy. Also implicit systems are incorporated in this framework. The link with H1 control is established through the scattering representation. Extensions to the distributed-parameter case are briefly indicated