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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 309–323 (Mi timm1102)  

This article is cited in 7 scientific papers (total in 7 papers)

On the question of construction of an attraction set under constraints of asymptotic nature

A. G. Chentsovab, A. P. Baklanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University

Abstract: We study a variant of the attainability problem with constraints of asymptotic nature on the choice of controls. More exactly, we consider a control problem in the class of impulses of given intensity and vanishingly small length. The situation is complicated by the presence of discontinuous dependences, which produces effects of the type of multiplying a discontinuous function by a generalized function. The constructed extensions in the special class of finitely additive measures make it possible to present the required solution, defined as an asymptotic analog of an attainability domain, in terms of a continuous image of a compact set, which is described with the use of the Stone space corresponding to the natural algebra of sets of the control interval.
One of the authors had the honor of communicating with Nikolai Nikolaevich Krasovskii for many years and discussed with him problems that led to the statement considered in the paper. Krasovskii's support of this research direction provided possibilities for its fruitful development. His disciples and colleagues will always cherish the memory of Nikolai Nikolaevich in their hearts.

Keywords: filter base, finitely additive measure, attraction set, generalized element, ultrafilter.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 40–55

Bibliographic databases:

UDC: 519.6
Received: 01.03.2014

Citation: A. G. Chentsov, A. P. Baklanov, “On the question of construction of an attraction set under constraints of asymptotic nature”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 309–323; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 40–55

Citation in format AMSBIB
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\paper On the question of construction of an attraction set under constraints of asymptotic nature
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 309--323
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 291
\issue , suppl. 1
\pages 40--55
\crossref{https://doi.org/10.1134/S0081543815090035}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Chentsov, “Abstraktnaya zadacha o dostizhimosti: “chisto asimptoticheskaya” versiya”, Tr. IMM UrO RAN, 21, no. 2, 2015, 289–305  mathnet  mathscinet  elib
    2. 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  mathnet  crossref  crossref  isi  elib
    3. A. G. Chentsov, “Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 102–118  mathnet  crossref  mathscinet  isi  elib
    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  mathnet  mathscinet  zmath  elib
    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  mathnet  crossref  elib
    6. E. G. Pytkeev, A. G. Chentsov, “Volmenovskii kompaktifikator i ego primenenie dlya issledovaniya abstraktnoi zadachi o dostizhimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 199–212  mathnet  crossref  elib
    7. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye sootnosheniya”, Izv. IMI UdGU, 53 (2019), 138–157  mathnet  crossref  elib
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