2024/10/31 by Francesca Anceschi, Giacomo Ascione, Anceschi, Francesca +5 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2410.24000
openalex publication_date 2024/10/31 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
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 Hölder and sublinearity conditions.