Port-Hamiltonian systems on graphs
For researchers in network dynamics and control, this provides a unified geometric framework that formalizes interconnection of port-Hamiltonian systems on graphs, though the approach is incremental as it extends existing port-Hamiltonian theory to graph-based systems.
This paper presents a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs, enabling systematic analysis and interconnection of networks. The framework is demonstrated on examples including consensus algorithms.
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and internal vertices. This allows for state variables associated to the edges, and formalizes the interconnection of networks. Examples from different origins such as consensus algorithms are shown to share the same structure. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis of the resulting dynamics.