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In this paper, the theory of the optimum control of an unknown linear plant is discussed. Rather than try to estimate the coeffcients of the plant, the future error as defined by a quadratic measure is estimated using a Bayesian estimator. In this manner, better system performance can be expected since the effect of estimation errors on the estimator is obtained. The optimum control signal is then obtained which minimizes the estimated future error. It is shown that it is a linear function of the present output of the system. In the final section, a necessary and sufficient condition is obtained for the convergence of this procedure to the optimum system obtained with known coefficients.