A Counterexample in Stochastic Optimum Control
Hans S. Witsenhausen · SIAM Journal on Control · 1968
It is sometimes conjectured that nothing is to be gained by using non-linear controllers when the objective is to minimize the expectation of a quadratic criterion for a linear system subject to Gaussian noise and with unconstrained control variables. In fact, this statement has only been established for the case where all control variables are generated by a single station which has perfect memory. Without this qualification the conjecture is false.