Selecting a Probability Distribution Density Applied to a Robust Control Problem

A refined statement of a probabilistic criterion control problem, appeared in the literature at the ridge of the centuries, is proposed and the corresponding approach to solve it is derived. The approach is oriented to taking into account conditions of existence of the resulting domain of the admissible controls (non emptiness of the intersections of the "partial" domains), as well as to provide the conditions of unambiguous selection of the "worst" probabilistic distribution(s) of the output variable of the plant model. As a basic analytical tool, probability theory inequalities are applied.