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Russia Yekaterinburg
Section  Mathematics 
Title  Unlocking of predicate: application to constructing a nonanticipating selection 
Author(s)  Serkov D.A.^{ab} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a}, Ural Federal University^{b} 
Abstract  We consider an approach to constructing a nonanticipating selection of a multivalued mapping; such a problem arises in control theory under conditions of uncertainty. The approach is called “unlocking of predicate” and consists in the reduction of finding the truth set of a predicate to searching fixed points of some mappings. Unlocking of predicate gives an extra opportunity to analyze the truth set and to build its elements with desired properties. In this article, we outline how to build “unlocking mappings” for some general types of predicates: we give a formal definition of the predicate unlocking operation, the rules for the construction and calculation of “unlocking mappings” and their basic properties. As an illustration, we routinely construct two unlocking mappings for the predicate “be nonanticipating mapping” and then on this base we provide the expression for the greatest nonanticipating selection of a given multifunction. 
Keywords  predicate unlocking, fixed points, nonanticipating mappings 
UDC  510.635, 517.988.52, 519.833, 517.977 
MSC  37N35, 65J15, 47J25, 52A01, 91A25 
DOI  10.20537/vm170211 
Received  1 February 2017 
Language  English 
Citation  Serkov D.A. Unlocking of predicate: application to constructing a nonanticipating selection, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 2, pp. 283291. 
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