Vanishing viscosity in mean-field optimal control

Abstract

We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on a vanishing viscosity method: we prove the convergence of the same problem where a diffusion term is added, with a small viscosity parameter. By using stochastic optimal control, we first show the existence of a sequence of optimal controls for the problem with diffusion. We then build the optimizer of the original problem by letting the viscosity parameter go to zero.

References in corpus (3)

• Mean-Field Sparse Optimal Control
• Differential Inclusions in Wasserstein Spaces: The Cauchy-Lipschitz Framework
• Vanishing viscosity for linear-quadratic mean-field control problems

Cited by in corpus (2)

• A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion
• Vanishing viscosity for linear-quadratic mean-field control problems