Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction

被引：2

作者：

Herzog, Roland ^{[1
]}

Pietschmann, Jan-Frederik ^{[2
]}

Winkler, Max ^{[3
]}

机构：

[1] Heidelberg Univ, Interdisciplinary Ctr Sci Comp, D-69120 Heidelberg, Germany

[2] Univ Augsburg, Chair Inverse Problems, D-86159 Augsburg, Germany

[3] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 88卷 / 03期

关键词：

Nonlinear PDEs; Eikonal equation; ODE-PDE coupling; Optimal control; Pedestrian motion; APPROXIMATION; EQUATIONS; DYNAMICS; VERSION; CROWDS;

D O I：

10.1007/s00245-023-10064-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

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页数：44

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