Further comments on "Adaptive stochastic control for a class of linear systems"

In the paper by Tse and Athans [1] an ad hoc control scheme was proposed which the authors claimed will converge to an asymptotically optimum control law. The proposition is based heavily on [1, theorem 1]. In a recent correspondence, Harunoglu and Brasch [2] give a counterexample indicating that [1, theorem 1] is incorrect. The purpose of this correspondence is to provide a correct statement for Theorem 1 and to develop an ad hoc control scheme which is asymptotically optimum.