Numerical approximation of high-dimensional optimal control problems

Luca Saluzzi - Scuola Normale Superiore
Numerical approximation of high-dimensional optimal control problems

Abstract
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. In this talk I will review some basics on optimal control problems and HJB equation and the challenges arising from its numerical approximation. The main disadvantage for this approach depends on the so-called curse of dimensionality, since the HJB equation and the dynamical system live in the same, possibly high dimensional, space. I will discuss possible strategies to tackle this problem based on tree structures, low rank approximation and model order reduction.