基于局部吸引的Hughes行人流模型的最优控制
Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction
摘要：
我们讨论了控制的人类群体的动力学是由一个正规化版本的休斯模型，比照。休斯：行人流动的连续统理论。交通研究B部分：方法，36（2002）。我们假设有限数量的代理人对人群采取行动，并试图在给定的时间间隔内优化他们的路径。目标泛函可以是一般的，它可以对应于，例如，快速疏散或保持一组个体的愿望。我们给出了正向模型的存在性结果，研究了控制-状态映射的可微性，建立了全局最优控制的存在性，并给出了最优性条件.
英文摘要：
We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes' model, cf. Hughes: A continuum theory for the flow of pedestrians. Transportation research part B: methodological, 36 (2002). 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 result for the forward model, 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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