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Real-time identification and control of linear discrete systems with Gauss-Markov random parameters and conditioned quadratic cost function are considered. Algorithms for explicit calculation of the identification and control are given for systems with perfect state measurement and are illustrated by example applications. The control strategy generated by the cost function is an identitication-adaptive controller which is continually revised as new data are received. The identification equations develop an explicit model of the system which is available for other purposes if desired, and can be used apart from the control context.