We provide a numerical realization of an optimal control problem for pedestrian motion with agents that was analyzed in Herzog et al. (Appl. Math. Optim. 88(3):87, 2023). 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.

我们提供了行人运动最优控制问题的数值实现，该问题在 Herzog 等人中进行了分析。(应用数学优化88(3):87, 2023)。该模型由休斯行人动力学模型的正则化变体组成，与常微分方程相结合，常微分方程描述了能够通过吸引力影响人群的主体的运动。我们设计了一种有限体积方案，保留模型固有的盒子约束，并讨论其一些属性。我们将我们的方案应用于针对疏散场景量身定制的目标函数。最后，对几个实际相关的几何形状进行了数值模拟。