Hybrid control for optimal visiting problems for a single player and for a crowd

TL;DR

This paper introduces a hybrid control approach for optimal visiting problems, enabling trajectory switching among targets, and extends it to a mean-field framework to analyze crowd behavior and fluxes.

Contribution

It presents a novel hybrid control method for visiting problems and adapts it to a mean-field model for crowd analysis, bridging discrete control and collective dynamics.

Findings

Hybrid control effectively manages trajectory switching between targets.

Mean-field adaptation models crowd fluxes and viability.

Framework supports multiple indistinguishable players.

Abstract

In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field framework to study viability and crowd fluxes to model a multitude of indistinguishable players.