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 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.