Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field - Archive ouverte HAL Access content directly
Journal Articles Journal of Differential Equations Year : 2020

Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field

Michel Duprez
Morgan Morancey
Francesco Rossi

Abstract

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no interaction between the agents. We give a characterization of the minimal time both for microscopic and macroscopic descriptions of a crowd. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control region to feed the desired final configuration. The construction of the control is explicit, providing a numerical algorithm for computing it. We finally give some numerical simulations.
Fichier principal
Vignette du fichier
MinTime.pdf (615.17 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01676679 , version 1 (05-01-2018)
hal-01676679 , version 2 (14-10-2018)
hal-01676679 , version 3 (27-11-2019)

Identifiers

  • HAL Id : hal-01676679 , version 3

Cite

Michel Duprez, Morgan Morancey, Francesco Rossi. Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field. Journal of Differential Equations, 2020, 269 (1). ⟨hal-01676679v3⟩
602 View
193 Download

Share

Gmail Facebook Twitter LinkedIn More