Top-level heading

Modelling vehicle and pedestrian dynamics with input-state-output port-Hamiltonian systems

Data e ora inizio evento
Data e ora fine evento
Sede

Dipartimento di Matematica Guido Castelnuovo, Università Sapienza Roma

Aula
Sala di Consiglio
Speaker ed affiliazione

Antoine Tordeux (University of Wuppertal)

Traffic flow and pedestrian crowds are complex phenomena characterised by different collective dynamics. Inspired by recent work in control engineering by Knorn et al. and Matei et al., we explore the application of input-state-output port-Hamiltonian systems for the modelling and analysis of pedestrian and vehicle dynamics. We first present a two-dimensional port-Hamiltonian pedestrian model, emphasizing the modelling components and their role in the dynamics. In particular, we investigate the emergence of collective behaviours such as lane formation in counterflow and stripe formation in crossflow through numerical simulations. Next, we analyse the dynamics of stochastic port-Hamiltonian road traffic models in one dimension. We focus on a quadratic interaction potential, where the system is a multidimensional Ornstein-Uhlenbeck process. The uncontrolled dynamics without input exhibit instability under stochastic perturbations. However, implementing an external speed control allows the system to stabilise and to converge weakly to Gaussian limit distributions. The convergence remains unconditional with constant speed control. Interestingly, a specific stability condition arises when the input control acts as a dynamic feedback depending on the distance ahead. This talk is based on joint work with Julia Ackermann, Matthias Ehrhardt, Thomas Kruse, Barbara Rüdiger, Claudia Totzeck and Baris Ugurcan.

Contatti/Organizzatori

giuseppe.visconti@uniroma1.it