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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 2, Pages 225–239 (Mi timm709)

One representation of the results of action of approximate solutions in a problem with constraints of asymptotic nature

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We consider an abstract attainability problem with constraints of asymptotic nature defined in the form of a nonempty family of subsets in the space of usual solutions. Various variants of implementing asymptotic effects are considered (convergence in a topological space, cycles, and so on). A rather general method is suggested for presenting the results of action of approximate solutions; this method generalizes constructions based on sequences in the space of usual solutions.

Keywords: attraction set, net, ultrafilter.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 276, suppl. 1, S48–S62

Bibliographic databases:

Document Type: Article
UDC: 519.6

Citation: A. G. Chentsov, “One representation of the results of action of approximate solutions in a problem with constraints of asymptotic nature”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 225–239; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S48–S62

Citation in format AMSBIB
\Bibitem{Che11} \by A.~G.~Chentsov \paper One representation of the results of action of approximate solutions in a~problem with constraints of asymptotic nature \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 2 \pages 225--239 \mathnet{http://mi.mathnet.ru/timm709} \elib{http://elibrary.ru/item.asp?id=17870035} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2012 \vol 276 \issue , suppl. 1 \pages S48--S62 \crossref{https://doi.org/10.1134/S0081543812020046} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305482900004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859324816} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. G. Chentsov, “Yarusnye otobrazheniya i preobrazovaniya na osnove ultrafiltrov”, Tr. IMM UrO RAN, 18, no. 4, 2012, 298–314
2. A. G. Chentsov, “On the question of representation of ultrafilters in a product of measurable spaces”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 65–78
3. A. G. Chentsov, “On the question of representation of ultrafilters and their application in extension constructions”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 29–48
4. A. G. Chentsov, “On certain problems of the structure of ultrafilters related to extensions of abstract control problems”, Autom. Remote Control, 74:12 (2013), 2020–2036
5. A. G. Chentsov, “Ultrafiltry izmerimykh prostranstv i ikh primenenie v konstruktsiyakh rasshirenii”, Tr. IMM UrO RAN, 20, no. 1, 2014, 285–304
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