Time: Friday, April 12, 2019

Time: 3:30 – 4:30 (coffee & refreshments starting at 3:00)

Place: HP 4351 (Macphail Room), School of Mathematics & Statistics, Carleton University

Speaker: Fabio Bagagiolo (University of Trento, Italy)

Title: Optimal control of the mean field game equilibrium for a pedestrian tourists’ flow model

Abstract:

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the historic center of a heritage city.

We initially present a mean field game model, where both continuous and switching decisional variables are introduced to respectively describe the position of a tourist and the point of interest that it may visit. We prove the existence of a mean field game equilibrium. A mean field game equilibrium is Nash-type equilibrium in the case of infinitely many players. Then, we study an optimization problem for an external controller who aims to induce a suitable mean field game equilibrium.

Short Bio: Fabio Bagagiolo is a tenured researcher in mathematical analysis at the University of Trento, Italy.

His research Interests include:

– Mathematical models of hysteresis and their analytical properties;

– Partial differential equations with hysteresis effects;

– Controllability of parabolic equations with hysteresis;

– Optimal control problems and differential games for ordinary differential equations and viscosity solutions of Hamilton-Jacobi equations;

– Hybrid systems;

– Mean field games.