Optimal control problems of nonlocal interaction equations
Analysis of PDEs
2022-05-19 v1
Abstract
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of individuals is described by a suitable nonlocal transport equation, while the role of the population of agents is designed by the optimal control problem. This model has been first studied in [12] for a class of continuous nonlocal potentials, while in the present project we consider the case of mildly singular potentials in a gradient flow formulation of the target transport equation.
Cite
@article{arxiv.2205.08921,
title = {Optimal control problems of nonlocal interaction equations},
author = {S. Fagioli and A. Kaufmann and E. Radici},
journal= {arXiv preprint arXiv:2205.08921},
year = {2022}
}