Minimal time problem for crowd models with a localized vector field

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 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.
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https://hal.archives-ouvertes.fr/hal-01676679
Contributeur : Michel Duprez <>
Soumis le : dimanche 14 octobre 2018 - 10:59:58
Dernière modification le : mardi 16 octobre 2018 - 01:19:05

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  • HAL Id : hal-01676679, version 2

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Michel Duprez, Morgan Morancey, Francesco Rossi. Minimal time problem for crowd models with a localized vector field. 2018. 〈hal-01676679v2〉

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