PORT-HAMILTONIAN STRUCTURE OF INTERACTING PARTICLE SYSTEMS AND ITS MEAN-FIELD LIMIT

We derive a minimal 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 us to characterize conserved quantities, such as Casimir functions, as well as the long-time behavior using a LaSalle-type argument on the particle level. It is then shown that the port-Hamiltonian structure is preserved in the mean-field limit, and an analogue of the LaSalle invariance principle is studied in the space of probability measures equipped with the 2-Wasserstein metric. The results on the particle and mean-field limit yield a new perspective on uniform stability of general interacting particle systems. Moreover, as the minimal port-Hamiltonian formulation is closed, we identify the ports of the subsystems which admit generalized mass-spring-damper structure modeling the binary interaction of two particles. Using the information about these ports, we discuss the coupling of difference species in a port-Hamiltonian preserving manner. © by SIAM.