Optimal control of the Fokker-Planck equation under state constraints in the Wasserstein space
Samuel Daudin
TL;DR
This paper develops optimal control conditions for the Fokker-Planck equation with state constraints in the Wasserstein space, linking to Mean Field Game systems and establishing regularity of controls.
Contribution
It introduces a novel approach to optimal control under state constraints in Wasserstein space, deriving conditions via a Mean Field Game framework.
Findings
Derived optimality conditions as a Mean Field Game system
Established Lipschitz regularity of optimal controls
Connected control problems with exclusion conditions in PDEs
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.
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Taxonomy
TopicsStochastic processes and financial applications · Geometric Analysis and Curvature Flows