2020/11/06 by Roland W. Herzog, Herzog, Roland, Jan‐Frederik Pietschmann +3
Engineering · Social Sciences · #Evacuation and Crowd Dynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2011.03580
openalex publication_date 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.