A numerical study of Witsenhausen's Counterexample

Abstract

In this thesis, we consider Witsenhausen's Counterexample, a two-stage control system in decentralized stochastic control. In particular, we investigate a specific homogenous integral equation that arises from the necessary first-order condition for optimality of the Stage I controller in the system. Using finite element (FE) analysis, we develop a numerical framework to study this integral equation and understand the structure of optimal controllers. We then solve the integral equation as a mathematical optimization and use our FE model to numerically compute a nonlinear controller that satisfies the necessary condition approximately at a set of quadrature points..