Project A10
Optimal control of McKean-Vlasov stochastic partial differential equations

Project description

We aim to systematically develop a variational approach to the control of McKean-Vlasov SPDEs. These SPDEs emerge as driving equations for asymptotic fluctuations in large interacting diffusing particle systems and provide probabilistic representations of certain nonlinear PDEs. Our goal is to derive existence results for optimal controls and optimality conditions, develop an adjoint calculus for the stochastic representation of cost functional gradients, and study the control of McKean-Vlasov equations with singular coefficients. A major application area is exploring the duality between optimal SPDE control and nonlinear stochastic filtering, and the numerical approximation of these systems. 

Principal Investigators

Nicolas Perkowski (FU Berlin)

Wilhelm Stannat (TU Berlin)

Project members

Liangying Chen (TU & FU Berlin)

Publications

Preprints

• Spille, J. B., & Stannat, W., 2025. Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations. https://doi.org/10.48550/ARXIV.2507.16288