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
|
- Warga J. Optimal control of differential and functional equations, New York: Academic Press, 1977.
- Chentsov A.G. Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature, Proceedings of the Steklov Institute of Mathematics, 2017, vol. 296, suppl. 1, pp. 102-118. https://doi.org/10.1134/S0081543817020109
- Chentsov A.G. An abstract reachability problem: “purely asymptotic” version, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2015, vol. 21, no. 2, pp. 289-305 (in Russian). http://mi.mathnet.ru/eng/timm1189
- Chentsov A.G. Filters and ultrafilters in the constructions of attraction sets, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, issue 1, pp. 113-142 (in Russian). https://doi.org/10.20537/vm110112
- Kuratowski K., Mostowski A. Set theory, Warsaw: PWN, 1967.
- Engelking R. General topology, Warsaw: PWN, 1977.
- Chentsov A.G., Morina S.I. Extensions and relaxations, Dordrecht: Springer, 2002.
- Chentsov A.G. Ultrafilters in the constructions of attraction sets: problem of compliance to constraints of asymptotic character, Differential Equations, 2011, vol. 47, no. 7, pp. 1059-1076. https://doi.org/10.1134/S0012266111070159
- Chentsov A.G. Asymptotic attainability, Dordrecht: Springer Netherlands, 1997. https://doi.org/10.1007/978-94-017-0805-0
- Chentsov A.G., Baklanov A.P. A problem related to asymptotic attainability in the mean, Doklady Mathematics, 2014, vol. 90, issue 3, pp. 762-765. https://doi.org/10.1134/S1064562414070333
- Chentsov A.G., Baklanov A.P. On an asymptotic analysis problem related to the construction of an attainability domain, Proceedings of the Steklov Institute of Mathematics, 2015, vol. 291, issue 1, pp. 279-298. https://doi.org/10.1134/S0081543815080222
- 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
|
Full text
|
|