Key points are not available for this paper at this time.
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.
H. S. Witsenhausen (Thu,) studied this question.