Optimal control of stochastic delay differential equations

PDE Seminar
Tuesday, January 31, 2023 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Filippo de Feo – Politecnico di Milano – filippo.defeo@polimi.it
Gong Chen

In this talk we will discuss an optimal control problem for stochastic differential delay equations. We will only consider the case with delays in the state. We will show how to rewrite the problem in a suitable infinite-dimensional Hilbert space. Then using the dynamic programming approach we will characterize the value function of the problem as the unique viscosity solution of an infinite dimensional Hamilton-Jacobi-Bellman equation.  We will discuss partial C^{1}-regularity of the value function. This regularity result is particularly interesting since it permits to construct a candidate optimal feedback map which may allow to find an optimal feedback control. Finally we will discuss some ideas about the case in which delays also appear in the controls.

This is a joint work with S. Federico and A. Święch.