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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1021283 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/102128 |
| Parent Title (English): | Applied Mathematics & Optimization |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/10/17 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/02/20 |
| Volume: | 88 |
| Issue: | 3 |
| First Page: | 87 |
| DOI: | https://doi.org/10.1007/s00245-023-10064-8 |
| 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) |
