Calculus of Variations and Geometric Measure Theory

M. Bongini - G. Buttazzo

Optimal Control Problems in Transport Dynamics

created by buttazzo on 26 Sep 2016


Submitted Paper

Inserted: 26 sep 2016
Last Updated: 26 sep 2016

Year: 2016


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.

Keywords: Wasserstein distance, optimal control problems, functionals on measures, transport dynamics