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arXiv · 1909.10596

On a Mean Field Optimal Control Problem

Jose A. Carrillo·Edgard A. Pimentel·Vardan K. Voskanyan
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Abstract

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.

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Jose A. Carrillo, Edgard A. Pimentel, Vardan K. Voskanyan. 2019-09-23. On a Mean Field Optimal Control Problem. https://arxiv.org/abs/1909.10596

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