2025/02/10 by Alain Bensoussan, P. Jameson Graber, Bensoussan, Alain +2
Engineering · #49N80 #Analysis of PDEs (math.AP) #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2502.07051
openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \citeCDLL, following the approach of control on Hilbert spaces introduced by the authors in \citeBGY-2. We include the common noise in this paper, so the alternative is now complete. Since we consider a control problem, our theory applies only to Mean field control and not to mean field games. The assumptions are adapted to guarantee a unique optimal control, so they insure that the cost functional is strictly convex and coercive.