Calculus of Variations and Geometric Measure Theory

S. Fagioli - A. Kaufmann - E. Radici

Optimal control problems of nonlocal interaction equations

created by radici on 28 Oct 2022
modified on 05 Jun 2024


Published Paper

Inserted: 28 oct 2022
Last Updated: 5 jun 2024

Journal: ESAIM: COCV
Year: 2023

ArXiv: 2205.08921 PDF


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.