Optimal Control Problems in Transport Dynamics

TL;DR

This paper formulates an optimal control problem in population dynamics, aiming to influence a target population's behavior through a controlled secondary population, with applications in crowd management, finance, and drone swarms.

Contribution

It introduces a novel optimal control framework for modifying population behaviors via interacting agents, applicable to various real-world scenarios.

Findings

Framework applicable to pedestrian movement control

Potential for influencing financial markets with minimal agents

Effective management of drone swarms using few piloted units

Abstract

In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with the first. The cost functional to be minimized to determine the dynamics of the second population takes into account the desired target or configuration to be reached as well as the quantity of control agents. Several applications may fall into this framework, as for instance driving a mass of pedestrian in (or out of) a certain location; influencing the stock market by acting on a small quantity of key investors; controlling a swarm of unmanned aerial vehicles by means of few piloted drones.