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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, Volume 31, Issue 1, Pages 70–88
DOI: https://doi.org/10.35634/vm210106
(Mi vuu756)
 

MATHEMATICS

Relaxation of the attainability problem for a linear control system of neutral type

A. G. Chentsovab, A. N. Sesekinab

a Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
b N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia
References:
Abstract: The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls — f.-a. measures. The structure of the mentioned AS is investigated.
Keywords: linear systems with time delay of neutral type, attraction sets, finitely additive measures.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00371
The study was funded by RFBR, projects number 19-01-00371.
Received: 11.01.2021
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 34A37, 34K06
Language: Russian
Citation: A. G. Chentsov, A. N. Sesekin, “Relaxation of the attainability problem for a linear control system of neutral type”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 70–88
Citation in format AMSBIB
\Bibitem{CheSes21}
\by A.~G.~Chentsov, A.~N.~Sesekin
\paper Relaxation of the attainability problem for a linear control system of neutral type
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 1
\pages 70--88
\mathnet{http://mi.mathnet.ru/vuu756}
\crossref{https://doi.org/10.35634/vm210106}
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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