Optimal control problems driven by nonlinear degenerate Fokker-Planck equations
Abstract
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as mean-field limits of Stochastic Differential models for multipopulation dynamics, where a large number of agents (followers) is steered through parsimonious intervention on a selected class of leaders. The proposed approach combines stability estimates for measure solutions of nonlinear degenerate Fokker-Planck equations with a general framework of assumptions on the cost functional, ensuring compactness and lower semicontinuity properties. The Lie structure of the state equations allows one for considering non-Lipschitz nonlinearities, provided some suitable dissipativity assumptions are considered in addition to non-Euclidean H\"{o}lder and sublinearity conditions.
Cite
@article{arxiv.2410.24000,
title = {Optimal control problems driven by nonlinear degenerate Fokker-Planck equations},
author = {Francesca Anceschi and Giacomo Ascione and Daniele Castorina and Francesco Solombrino},
journal= {arXiv preprint arXiv:2410.24000},
year = {2024}
}