M. Rotkowitz
Linear Controllers are Uniformly Optimal for the Witsenhausen Counterexample
Proceedings of the IEEE Conference on Decision and Control, pp. 553-558, December 2006.

Abstract

In 1968, Witsenhausen introduced his celebrated counterexample, which illustrated that when an information pattern is nonclassical, the controllers which optimize an expected quadratic cost may be nonlinear. It is shown here that for the Witsenhausen Counterexample, when one instead considers the induced norm, then linear controllers are in fact optimal.