On pedestrian dnamics: modelling, control, and simulation
File(s)
Author(s)
Sanchez Bailo, Rafael Tomas
Type
Thesis
Abstract
This thesis concerns the modelling, control, and simulation of pedestrian dynamics. We begin by constructing a new microscopic, agent-based model which attempts to reproduce the rational behaviour of individual agents through the means of anticipation. Each pedestrian undergoes a two-step time evolution based on a perception stage and a decision stage. We continue by studying the consensus control of agent-based models, in both the smooth and non-smooth penalisation settings. The first is computed through gradient methods and studied in the mean-field limit; the second is aproximated through model-predictive control. Later, we propose a new family of macroscopic models for pedestrian dynamics, inspired by the literature of traffic modelling. The models include a singular congestion term, which ensures that the crowd density remains below a given physical capacity parameter. To capture the constrained behaviour, we propose asymptotic-preserving schemes with first and second-order accuracy. In the macroscopic regime, we consider a more general family of models for agent systems, and propose structure-preserving schemes which capture the energy dissipation of the system at the fully discrete level. The schemes are generalised to higher dimensions through sweeping dimensional splitting. To conclude, we prove the convergence of the fully implicit scheme.
Version
Open Access
Date Issued
2020-05
Date Awarded
2020-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Carrillo de la Plata, Jose Antonio
Degond, Pierre
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
1835367
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)