Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction

TL;DR

This paper develops an optimal control framework for pedestrian flow modeled by Hughes' continuum model, incorporating local attractions and agent-based path optimization, with theoretical guarantees for existence and optimality conditions.

Contribution

It introduces a control approach for Hughes' pedestrian flow model with finite agents, proving existence of solutions and deriving optimality conditions.

Findings

Existence of solutions for the forward model.

Differentiability of the control-to-state map.

Existence of a globally optimal control.

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.