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 (Transp Res Part B: Methodol 36(6):507-535, 2002. https://doi.org/10.1016/s0191-2615(01)00015-7). We assume that a finite number of agents act on the crowd and try to optimize the...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 October 2023
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| In: |
Applied mathematics & optimization
Year: 2023, Volume: 88, Issue: 3, Pages: 1-44 |
| ISSN: | 1432-0606 |
| DOI: | 10.1007/s00245-023-10064-8 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00245-023-10064-8
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| Author Notes: | Roland Herzog, Jan-Frederik Pietschmann, Max Winkler |
| Summary: | We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes’ model, cf. Hughes (Transp Res Part B: Methodol 36(6):507-535, 2002. https://doi.org/10.1016/s0191-2615(01)00015-7). 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 and regularity result for the coupled PDE-ODE forward model via an approximation argument, 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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| Item Description: | Gesehen am 08.05.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1432-0606 |
| DOI: | 10.1007/s00245-023-10064-8 |