Optimal control of Hughes’ model for pedestrian flow via local attraction

• Verfasst von: Herzog, Roland [VerfasserIn]
• Verfasst von: Pietschmann, Jan-Frederik [VerfasserIn]
• Verfasst von: Winkler, Max [VerfasserIn]
• Titel: Optimal control of Hughes’ model for pedestrian flow via local attraction
• Verf.angabe: Roland Herzog, Jan-Frederik Pietschmann, Max Winkler
• E-Jahr: 2023
• Jahr: 17 October 2023
• Umfang: 44 S.
• Fussnoten: Gesehen am 08.05.2024
• Titel Quelle: Enthalten in: Applied mathematics & optimization
• Ort Quelle: New York, NY : Springer, 1974
• Jahr Quelle: 2023
• Band/Heft Quelle: 88(2023), 3, Artikel-ID 87, Seite 1-44
• ISSN Quelle: 1432-0606
• DOI: doi:10.1007/s00245-023-10064-8
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 35K20
• Sach-SW: 35Q93
• Sach-SW: 49J20
• Sach-SW: 92D50
• Sach-SW: Eikonal equation
• Sach-SW: Nonlinear PDEs
• Sach-SW: ODE-PDE coupling
• Sach-SW: Optimal control
• Sach-SW: Pedestrian motion
• K10plus-PPN: 1888102195

Abstract

We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes’ model, cf. Hughes (Transp Res Part B: Methodol 36(6):507-535, 2002. https://doi.org/10.1016/s0191-2615(01)00015-7). We assume that a finite number of agents act on the crowd and try to optimize their paths in a given time interval. The objective functional can be general and it can correspond, for instance, to the desire for fast evacuation or to maintain a single group of individuals. We provide an existence and regularity result for the coupled PDE-ODE forward model via an approximation argument, study differentiability properties of the control-to-state map, establish the existence of a globally optimal control and formulate optimality conditions.