Identification and control of linear discrete-time systems with unknown time-invariant parameters and conditional quadratic cost function are considered. Parameters of the system are unknown but subject to a given aprioridistribution. A multi-step control algorithm is developed for systems given only noisy output measurements. The control strategy generated by the algorithm is continuously revised as new data are received. An example is solved to illustrate the method. It is shown that revision of control strategies, as new data become available, requires solution of a set of recurrence coefficient equations.