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.
| Author: | Roland Herzog, Jan-Frederik PietschmannGND, Max Winkler |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/102128 |
| Parent Title (English): | arXiv |
| Publisher: | arXiv |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2020 |
| Release Date: | 2023/02/20 |
| Issue: | arXiv:2011.03580 |
| DOI: | https://doi.org/10.48550/arXiv.2011.03580 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme | |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
