In this paper we join the previous results about asymptotic properties of a randomized control strategy with new one based on a non-asymptotic approach of LSCR (Leave-out Sign-dominant Correlation Regions) methods. Our consideration is focused on problems of the identification or adaptive optimal control for the linear plant with unknown parameters and dynamics disturbed by an external noise. The assumptions about the noise are reduced to a minimum: it can virtually be arbitrary, but, independently of it, the user must be able to add test perturbations through the input channel. The theoretical results are illustrated by simulations.