  In this paper we present an optimal control approach modeling fast exit
scenarios in pedestrian crowds. In particular we consider the case of a large
human crowd trying to exit a room as fast as possible. The motion of every
pedestrian is determined by minimizing a cost functional, which depends on
his/her position, velocity, exit time and the overall density of people. This
microscopic setup leads in the mean-field limit to a parabolic optimal control
problem. We discuss the modeling of the macroscopic optimal control approach
and show how the optimal conditions relate to Hughes model for pedestrian flow.
Furthermore we provide results on the existence and uniqueness of minimizers
and illustrate the behavior of the model with various numerical results.
