Port-Hamiltonian systems represent an important and attractive novel paradigm for the mathematical mode­ling of dynamical systems. In contemporary research, the focus currently shifts from the analysis and treatment of closed systems to the interaction between multiple systems. In such networks of dynamical systems, the single constituents can be of very different nature, and it is the port-Hamiltonian paradigm with its distinguished emphasis on internal and external ports that allows for a universal mathematical description of the coupling between diverse systems while preserving crucial system properties. For example — and very importantly — port-Hamiltonian coupling genuinely guarantees stability of the overall system when the individual systems are stable, a feature that is lacking in other coupling approaches.

The core of the port-Hamiltonian paradigm is a generalized concept of energy together with its flow along internal connections and external power-conjugate input and output ports. The conservation or dissipation properties of the modeling components as well as the identification of external ports play a central role. External ports allow, in particular, for a recursive coupling of mathematical models across different scales and domains. The generalized energy is encoded in the Hamiltonian, and the ports are defined by a Dirac structure. Together they provide the canonical framework for coupling and for the preservation of characteristic properties.

Port-Hamiltonian systems currently evolve into an extremely powerful modeling tool for abstract dynamical systems leading to unprecedented progress in their mathematical analysis, their simulation and their optimization. To fully exploit the mathematical potential of port-Hamiltonian systems we thus need contributions from multiple mathematical disciplines. This interdisciplinary challenge is addressed by the Port-Hamiltonian Institute.