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Russia Yekaterinburg
Section Mathematics
Title Unlocking of predicate: application to constructing a non-anticipating selection
Author(-s) Serkov D.A.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract We consider an approach to constructing a non-anticipating 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 non-anticipating mapping” and then on this base we provide the expression for the greatest non-anticipating 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 non-anticipating selection, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 2, pp. 283-291.
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