  Port-Hamiltonian systems (PHS) theory is a recent but already
well-established modelling approach for non-linear physical systems. Some
studies have shown lately that PHS frameworks are relevant for modelling and
control of swarm and multi-agent systems. We identify in this contribution a
general class of microscopic force-based pedestrian models that can be
formulated as a port-Hamiltonian system. The pedestrian PHS has linear
structure and dissipation components. Non-linear effects come from isotropic
pedestrian interactions. Simulation results on a torus with disordered initial
states show that the port-Hamiltonian pedestrian model can exhibit different
types of dynamics. They range from relaxed speed models with no interaction,
dynamical billiards, or crystallization dynamics to realistic pedestrian
collective behaviors, including lane and strip formation for counter and
crossing flow. The port-Hamiltonian framework is a natural multiscale
description of pedestrian dynamics as the Hamiltonian turns out to be a generic
order parameter that allows us to identify specific behaviours of the dynamics
from a macroscopic viewpoint. Particular cases even enable through energy
balance to determine the Hamiltonian behavior without requiring the tedious
computation of the microscopic dynamics. Using PHS theory, we systematically
identify a critical threshold value for the Hamiltonian, which relies only on
exogenous input and can be physically interpreted.
