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Russia Yekaterinburg
Year
2019
Volume
29
Issue
4
Pages
569-582
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Section Mathematics
Title Constraints of asymptotic nature and attainability problems
Author(-s) Chentsov A.G.ab, Pytkeev E.G.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract In control problems, construction and investigation of attainability domains and their analogs are very important. This paper addresses attainability problems in topological spaces. Constraints of asymptotic nature defined in the form of nonempty families of sets are used. The solution of the corresponding attainability problem is defined as an attraction set. Points of this attraction set (attraction elements) are realized in the class of approximate solutions which are nonsequential analogs of the Warga approximate solutions. Some possibilities of applying compactifiers are discussed. Questions of the realization of attraction sets up to a given neighborhood are considered. Some topological properties of attraction sets are investigated. An example with an empty attraction set is considered.
Keywords attraction set, extension, topological space, compactness
UDC 517.9
MSC 28A33
DOI 10.20537/vm190408
Received 28 August 2019
Language English
Citation Chentsov A.G., Pytkeev E.G. Constraints of asymptotic nature and attainability problems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 569-582.
References
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  12. Chentsov A.G., Baklanov A.P., Savenkov I.I. A problem of attainability with constraints of asymptotic nature, Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2016, issue 1 (47), pp. 54-118 (in Russian). http://mi.mathnet.ru/eng/iimi328
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