On the separation property in a priori problems of ensured control and estimation. Operator formalization

In a priori problems of optimal ensured control-estimation with the extremal quality criterion, formalization of the separation property is considered on the basis of simmetrized operator representation in Hilbert spaces. Sufficient conditions, in the form of operator equations, are presented, for the separation property to hold. Some weaker property, which is an analog of certainty equivalence is also considered.