Port-Hamiltonian approach to interacting particle systems

Next Tuesday June 20, 2023 we have as part of the Mathematisches Kolloquium at our Faculty of Sciences at FAU:

Port-Hamiltonian approach to interacting particle systems

By Prof. Dr. Birgit Jacob, Bergische Universität Wuppertal

Host: Our Akad. Dir. Prof. Dr. Martin Gugat

Abstract. Port-Hamiltonian systems represent an important and attractive novel paradigm for the mathematical modeling of dynamical systems. 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. We derive a port-Hamiltonian formulation of a general class of interacting particle systems driven by alignment and potential-based force dynamics which include the Cucker-Smale model with potential interaction and the second order Kuramoto model. The port-Hamiltonian structure allows to characterize conserved quantities such as Casimir functions as well as the long-time behaviour using a LaSalle-type argument on the particle level. Futher, the port-Hamiltonian structure is preserved in the mean-field limit.

WHERE

HS H13

FAU. Department Mathematik

Cauerstr. 11, Erlangen