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 Avtomat. i Telemekh., 2013, Issue 12, Pages 119–139 (Mi at6173)

Topical issue

On certain problems of the structure of ultrafilters related to extensions of abstract control problems

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

Abstract: We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints.

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English version:
Automation and Remote Control, 2013, 74:12, 2020–2036

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: V. I. Gurman

Citation: A. G. Chentsov, “On certain problems of the structure of ultrafilters related to extensions of abstract control problems”, Avtomat. i Telemekh., 2013, no. 12, 119–139; Autom. Remote Control, 74:12 (2013), 2020–2036

Citation in format AMSBIB
\Bibitem{Che13} \by A.~G.~Chentsov \paper On certain problems of the structure of ultrafilters related to extensions of abstract control problems \jour Avtomat. i Telemekh. \yr 2013 \issue 12 \pages 119--139 \mathnet{http://mi.mathnet.ru/at6173} \transl \jour Autom. Remote Control \yr 2013 \vol 74 \issue 12 \pages 2020--2036 \crossref{https://doi.org/10.1134/S0005117913120060} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000328621300006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891516494} 

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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, A. P. Baklanov, “On the question of construction of an attraction set under constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 40–55
2. Chentsov A.G., Baklanov A.P., “a Problem Related To Asymptotic Attainability in the Mean”, Dokl. Math., 90:3 (2014), 762–765
3. A. G. Chentsov, A. P. Baklanov, “On an asymptotic analysis problem related to the construction of an attainability domain”, Proc. Steklov Inst. Math., 291 (2015), 279–298
4. A. G. Chentsov, A. P. Baklanov, I. I. Savenkov, “Zadacha o dostizhimosti s ogranicheniyami asimptoticheskogo kharaktera”, Izv. IMI UdGU, 2016, no. 1(47), 54–118
5. A. G. Chentsov, I. I. Savenkov, Yu. V. Shapar, “Odna zadacha na programmnyi maksimin pri ogranicheniyakh impulsnogo kharaktera”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 91–110
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