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Izv. IMI UdGU, 2016, Issue 1(47), Pages 54–118 (Mi iimi328)  

This article is cited in 2 scientific papers (total in 2 papers)

A problem of attainability with constraints of asymptotic nature

A. G. Chentsovab, A. P. Baklanovb, I. I. Savenkovb

a Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: We construct and study properties of attainability sets for a linear control system with discontinuous coefficients of the control action. This problem is tightly connected with the issue of an attainability “on average” (i.e. the type of an attainability in the class of mathematical expectations of random vectors). Focusing on the case of constraints of an asymptotic character, we tackle the mentioned problems by means of the universal approach. These constraints correspond to a control regime in the class of “narrow” pulses. We consider a control problem in the class of pulse-like controls complying with the requirement of full consumption of energy resources.

Keywords: attraction set, topological space, ultrafilter.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07909_а
16-01-00505_а


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Bibliographic databases:

Document Type: Article
UDC: 517.9
MSC: 49N05, 54H99
Received: 15.01.2016

Citation: A. G. Chentsov, A. P. Baklanov, I. I. Savenkov, “A problem of attainability with constraints of asymptotic nature”, Izv. IMI UdGU, 2016, no. 1(47), 54–118

Citation in format AMSBIB
\Bibitem{CheBakSav16}
\by A.~G.~Chentsov, A.~P.~Baklanov, I.~I.~Savenkov
\paper A problem of attainability with constraints of asymptotic nature
\jour Izv. IMI UdGU
\yr 2016
\issue 1(47)
\pages 54--118
\mathnet{http://mi.mathnet.ru/iimi328}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3512915}
\zmath{https://zbmath.org/?q=an:1379.49029}
\elib{http://elibrary.ru/item.asp?id=25980777}


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    This publication is cited in the following articles:
    1. 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
    2. 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
  • Известия Института математики и информатики Удмуртского государственного университета Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
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