Article Dans Une Revue Journal of Differential Equations Année : 2020

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

Michel Duprez
Francesco Rossi

Résumé

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.

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Cite 10.1016/j.jde.2019.11.098 Autre Duprez, M., Morancey, M., & Rossi, F. (2020). Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field. Journal of Differential Equations, 269(1), 82–124. https://doi.org/10.1016/j.jde.2019.11.098

Dates et versions

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

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  • HAL Id : hal-01676679 , version 3

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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⟩
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