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The control of a stochastic system with unknown parameters is considered. A novel cost function which includes the variance of the innovations process is used to optimize the performance of the system. The cost function has two parts. One that reflects the goal of regulating the output, and the second one that reflects the need to gather as much information as possible about the parameters of the system, the latter being represented by the variance of the innovation process. The control law derived has an explicit solution that allows for an easy implementation, and has dual properties. The relationships among the controller obtained in this paper and the certainty equivalence and cautious controllers are analyzed. Simulation results show the quasi-optimal performance of the new controller.