Calculus of Variations and Geometric Measure Theory

G. Ascione - D. Castorina - F. Solombrino

Mean field sparse optimal control of systems with additive white noise

created by solombrino on 06 Apr 2022
modified on 06 Nov 2023


Published Paper

Inserted: 6 apr 2022
Last Updated: 6 nov 2023

Journal: Siam Journal on Mathematical Analysis
Volume: 55
Number: 6
Pages: 6965-6990
Year: 2023

ArXiv: 2204.02431 PDF
Links: ArXiv preprint


We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a SDE constraint, we introduce a rigorous limit process towards an infinite dimensional optimal control problem constrained by the coupling of a system of ODE for the leaders with a McKean-Vlasov-type SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the $\Gamma$-limit of the cost functionals for the finite dimensional problems.