Department of Computer, Control and Management Engineering

Port-Hamiltonian systems offer a unified framework for the modeling, simulation and control of physical systems from different domains. On the other hand, maximal monotone relations appear in many areas of convex analysis and optimization, as well as in input-output system analysis. In this talk the relationship of the theory of port-Hamiltonian systems with the concept of monotonicity is explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to systems defined with respect to maximal cyclically monotone relations, together with their generating convex functions. This gives rise to interesting subclasses of systems, with examples stemming from physical systems modeling as well as from convex optimization. Furthermore, maximal monotone and maximal cyclically monotone relations can be shown to be compositional, where in the second case the resulting maximal cyclically monotone relation is computable through the use of generating functions. These results on compositionality are employed for steady state analysis and a convex optimization approach to the computation of the equilibria of interconnected incrementally port-Hamiltonian systems. Finally, the relation with incremental and differential passivity is discussed, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are equilibrium independent passive. Based on joint work with Kanat Camlibel