Fabio Bagagiolo — Page 2

arXiv2019

Optimal control of the mean field equilibrium for a pedestrian tourists' flow model

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 he/she may visit. We prove the existence of a mean field equilibrium. A mean field 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 equilibrium.

math.OC↗

arXiv2016

Swimming by switching

In this paper we investigate different strategies to overcome the scallop theorem. We will show how to obtain a net motion exploiting the fluid's type change during a periodic deformation. We are interested in two different models: in the first one that change is linked to the magnitude of the opening and closing velocity. Instead, in the second one it is related to the sign of the above velocity. An interesting feature of the latter model is the introduction of a delay-switching rule through a thermostat. We remark that the latter is fundamental in order to get both forward and backward motion.

math.DS↗