基于保结构有限体积法的智能体控制行人动力学数值研究
Numerical investigation of agent controlled pedestrian dynamics using a structure preserving finite volume scheme
摘要：
我们提供了行人运动的最优控制问题的数值实现，该问题在Herzog，Pietschmann，Winkler：“通过局部吸引力对Hughes行人流模型的最优控制”中进行了分析。“，arXiv 2011.03580，2020.该模型由Hughes行人动力学模型的正则化变体和描述能够通过吸引力影响人群的代理运动的常微分方程组成。我们设计了一个有限体积的计划，保留了盒子的约束，在模型中固有的，并讨论了它的一些属性。我们将我们的计划适用于一个目标功能的情况下，疏散方案。最后，对几种实际相关的几何形状进行了数值模拟。
英文摘要：
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.
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