Minimal time problem for crowd models with a localized vector field

Michel Duprez (1) , Morgan Morancey (1) , Francesco Rossi (2)

1 I2M - Institut de Mathématiques de Marseille
2 LSIS - Laboratoire des Sciences de l'Information et des Systèmes

In this work, we study the minimal time to steer a crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd displacement, localized on a fixed control set. We give a characterization of the minimal time both for discrete and continuous crowds. 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 then provide some examples of numerical simulations.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Michel Duprez, Morgan Morancey, Francesco Rossi. Minimal time problem for crowd models with a localized vector field. 2018. ⟨hal-01676679v1⟩