On a mean field optimal control problem

José A. Carrillo, Edgard A. Pimentel, Vardan K. Voskanyan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper we consider a mean field optimal control problem with an aggregation–diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a Hamilton–Jacobi and a Fokker–Planck equation, describing the optimal control aspect of the problem and the evolution of the population of agents, respectively. The main contribution of the paper is a result on the existence of solutions for the aforementioned system. We notice this model is in close connection with the theory of mean-field games systems. However, a distinctive feature concerns the nonlocal character of the interaction; it affects the drift term in the Fokker–Planck equation as well as the Hamiltonian of the system, leading to new difficulties to be addressed.
Original languageEnglish (US)
Pages (from-to)112039
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - Jun 30 2020
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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