On the operator formalization of the separation property in ensured control problems

The separation principle and the certainty equivalence property in ensured problems of control/estimation optimal are considered. Problems under discussion are stated for linear uncertain systems with unknown in advance parameters, lndeces of performance are given by extremal values of a convex functional. A priori procedures of control and estimation are supposed to be determined by the choice of causal (nonanticipative) operators. Investigation is based on a symmetrical representation of extremal problems in Hilbert spaces. Formalized definitions of the separation and certainty equivalence properties are given. Conditions on elements of a problem structure sufficient for the properties to hold are presented.