We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv 2011.03580, 2020. The model consists of a regularized variant of Hughes' model for pedestrian dynamics coupled to ordinary differential equations that describe the motion of agents which are able to influence the crowd via attractive forces. We devise a finite volume scheme that preserves the box constraints that are inherent in the model and discuss some of its properties. We apply our scheme to an objective functional tailored to the case of an evacuation scenario. Finally, numerical simulations for several practically relevant geometries are performed.
翻译：在Herzog、Pietschmann、Winkler Herzog中分析的代理物对行人运动的最佳控制问题,我们从数字上实现了最佳控制问题。 “最佳控制Hughes' Pedestrian Flow 模型通过本地吸引物进行最佳控制 ”, ArXiv 2011-03580, 2020。该模型由休斯的行人动态模型的正规变体组成,加上描述能够通过有吸引力的力量影响人群的代理物动作的普通差异方程式。我们设计了一个有限的体积计划,保留模型中固有的框框限制,并讨论其中的一些特性。我们用我们的计划来设计一个符合疏散情景的客观功能。最后,对几个实际相关的地貌进行了数字模拟。
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