Optimal control of Hughes' model for pedestrian flow via local attraction

  • 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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Author:Roland Herzog, Jan-Frederik PietschmannORCiDGND, Max Winkler
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/102128
Parent Title (English):Applied Mathematics & Optimization
Publisher:Springer Science and Business Media LLC
Date of first Publication:2023/10/17
Publishing Institution:Universität Augsburg
Release Date:2023/02/20
First Page:87
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)