# Optimal control of the Fokker-Planck equation under state constraints in the Wasserstein space

arXiv: https://arxiv.org/abs/2109.14978 · HTML: https://mlsanity.com/paper/2109.14978/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2021.

## Built on by (most cited first, 2 of 2)

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## Abstract (arXiv)

We analyze a problem of optimal control of the Fokker-Planck equation with state constraints in the Wasserstein space of probability measures. Our main result is to derive optimality conditions in the form of a Mean Field Game system of partial differential equations completed with an exclusion condition. As a by-product we obtain the Lipschitz regularity of optimal controls.