Till innehåll på sidan
Till KTH:s startsida

Topics in the mean-field type approach to pedestrian crowd modeling and conventions

Tid: Må 2019-12-16 kl 10.00

Plats: Kollegiesalen, Brinellvägen 8, Stockholm (English)

Respondent: Alexander Aurell , Matematisk statistik

Opponent: Professor Roland Malhamé, Polytechnique Montréal, Montréal, Canada

Handledare: Professor Boualem Djehiche, Matematisk statistik; Professor Xiaoming Hu, Optimeringslära och systemteori

Exportera till kalender

Abstract

This thesis consists of five appended papers, primarily addressingtopics in pedestrian crowd modeling and the formation of conventions.The first paper generalizes a pedestrian crowd model for competingsubcrowds to include nonlocal interactions and an arbitrary (butfinite) number of subcrowds. Each pedestrian is granted a ’personalspace’ and is effected by the presence of other pedestrians within it.The interaction strength may depend on subcrowd affinity. The paperinvestigates the mean-field type game between subcrowds and derivesconditions for the reduction of the game to an optimization problem.The second paper suggest a model for pedestrians with a predeterminedtarget they have to reach. The fixed and non-negotiablefinal target leads us to formulate a model with backward stochasticdifferential equations of mean-field type. Equilibrium in the game betweenthe tagged pedestrians and a surrounding crowd is characterizedwith the stochastic maximum principle. The model is illustrated by anumber of numerical examples.The third paper introduces sticky reflected stochastic differentialequations with boundary diffusion as a means to include walls andobstacles in the mean-field approach to pedestrian crowd modeling.The proposed dynamics allow the pedestrians to move and interactwhile spending time on the boundary. The model only admits a weaksolution, leading to the formulation of a weak optimal control problem.The fourth paper treats two-player finite-horizon mean-field typegames between players whose state trajectories are given by backwardstochastic differential equations of mean-field type. The paper validatesthe stochastic maximum principle for such games. Numericalexperiments illustrate equilibrium behavior and the price of anarchy.The fifth paper treats the formation of conventions in a large populationof agents that repeatedly play a finite two-player game. Theplayers access a history of previously used action profiles and form beliefson how the opposing player will act. A dynamical model wheremore recent interactions are considered to be more important in thebelief-forming process is proposed. Convergence of the history to acollection of minimal CURB blocks and, for a certain class of games,to Nash equilibria is proven.

urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-263759