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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 168, Pages 105–113
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This article is cited in 1 scientific paper (total in 1 paper)
Control of a discrete dynamic system with noise
V. I. Ukhobotov, S. A. Nikitina Chelyabinsk State University
Abstract:
For a discrete dynamic controlled system with noise, we consider the problem of retaining a phase point in a given family of sets at discrete instants of time. We analyze the case where the control vectogram is a polyhedron defined by a system of linear inequalities. We prove some properties of specific polyhedra satisfying the linearity condition, which allows us to obtain a condition of retention in the explicit form. Necessary and sufficient conditions for the possibility of retention are given. The results obtained are illustrated by an example.
Keywords:
discrete system, multi-step control problem, polyhedron of control values
DOI:
https://doi.org/10.36535/0233-6723-2019-168-105-113
Full text:
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UDC:
517.977
MSC: 93C41, 93C55
Citation:
V. I. Ukhobotov, S. A. Nikitina, “Control of a discrete dynamic system with noise”, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 168, VINITI, Moscow, 2019, 105–113
Citation in format AMSBIB
\Bibitem{UkhNik19}
\by V.~I.~Ukhobotov, S.~A.~Nikitina
\paper Control of a discrete dynamic system with noise
\inbook Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25--28, 2018. Part 1
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 168
\pages 105--113
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into506}
\crossref{https://doi.org/10.36535/0233-6723-2019-168-105-113}
Linking options:
http://mi.mathnet.ru/eng/into506 http://mi.mathnet.ru/eng/into/v168/p105
Citing articles on Google Scholar:
Russian citations,
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Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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S. A. Nikitina, V. I. Ukhobotov, “Ob odnoi zadache upravleniya zapasami pri nalichii pomekhi”, Chelyab. fiz.-matem. zhurn., 5:3 (2020), 306–315
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