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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 168, Pages 105–113 (Mi into506)  

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

Funding Agency Grant Number
Russian Foundation for Basic Research No~18-01-00264a
This work was supported by the Russian Foundation for Basic Research (project No. 18-01-00264a).


DOI: https://doi.org/10.36535/0233-6723-2019-168-105-113

Full text: PDF file (180 kB)
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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}


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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. S. A. Nikitina, V. I. Ukhobotov, “Ob odnoi zadache upravleniya zapasami pri nalichii pomekhi”, Chelyab. fiz.-matem. zhurn., 5:3 (2020), 306–315  mathnet  crossref
  • Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory" Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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