Optimal control of the Fokker-Planck equation under state constraints in the Wasserstein space
Abstract
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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.