Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction
Optimization and Control
2020-11-10 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2011.03580,
title = {Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction},
author = {Roland Herzog and Jan-Frederik Pietschmann and Max Winkler},
journal= {arXiv preprint arXiv:2011.03580},
year = {2020}
}