Title: Stochastic optimal control in infinite dimensions: verification and optimal synthesis

 

Abstract: In this talk, we consider a finite-horizon optimal control problem governed by stochastic evolution equations. First, we give a brief introduction to the dynamic programming approach. Then, we present a verification theorem for fully nonlinear Hamilton-Jacobi-Bellman equations in the framework of viscosity solutions. In the second part of the talk, we show how to obtain higher regularity of the value function, and use this regularity result to perform optimal synthesis, i.e., we construct optimal control in feedback form. This talk is based on [W. Stannat, L. Wessels: Necessary and Sufficient Conditions for Optimal Control of Semilinear Stochastic Partial Differential Equations, https://arxiv.org/abs/2112.09639, 2023] and [F. De Feo, A. Swiech, L. Wessels: Stochastic Optimal Control in Hilbert Spaces: \(C^{1,1}\)-Regularity of the Value Function and Optimal Synthesis via Viscosity Solutions, https://arxiv.org/abs/2310.03181, 2023]

 

 

Host: Yuming Paul Zhang