We consider an approach to constructing a non-anticipating selection of amultivalued mapping; such a problem arises in control theory under conditionsof uncertainty. The approach is called "unlocking of predicate" and consists inthe reduction of finding the truth set of a predicate to searching fixed pointsof some mappings. Unlocking of predicate gives an extra opportunity to analyzethe truth set and to build its elements with desired properties. In this article, we outline how to build "unlocking mappings" for somegeneral types of predicates: we give a formal definition of the predicateunlocking operation, the rules for the construction and calculation of"unlocking mappings" and their basic properties. As an illustration, weroutinely construct two unlocking mappings for the predicate "benon-anticipating mapping" and then on this base we provide the expression forthe greatest non-anticipating selection of a given multifunction.
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