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 Chelyab. Fiz.-Mat. Zh., 2018, Volume 3, Issue 3, Pages 311–318 (Mi chfmj107)

Mathematics

On a control problem for a discrete system

S. A. Nikitina, A. S. Scorynin, V. I. Ukhobotov

Chelyabinsk State University

Abstract: The article proposes one of the approaches for solving the control problem of a linear discrete system. A conflict-controlled process is considered whose duration is given. It is required that at the end of the control process the phase point is contained in a given set. Rules governing the control of a discrete system contain discrimination for the second player. The case is considered when the control vector and a given set are polyhedra given by a system of linear inequalities. It is assumed that for polyhedra a certain property of linearity is satisfied, which makes it possible to obtain the solution of the problem explicitly. The operator of operator absorption is introduced into the consideration in the paper. With the help of this operator, conditions are written for a set of initial positions under which the required inclusion is guaranteed at the time of the end of the control process. These conditions are written in the form of a system of inequalities. The practical part of the work shows the application of the obtained results to economic systems. The solution of the problem of inventory management is given.

Keywords: discrete system, multi-step control problem, polyhedral control set, inventory management problem.

DOI: https://doi.org/10.24411/2500-0101-2018-13304

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Revised: 29.07.2018

Citation: S. A. Nikitina, A. S. Scorynin, V. I. Ukhobotov, “On a control problem for a discrete system”, Chelyab. Fiz.-Mat. Zh., 3:3 (2018), 311–318

Citation in format AMSBIB
\Bibitem{NikSkoUkh18} \by S.~A.~Nikitina, A.~S.~Scorynin, V.~I.~Ukhobotov \paper On a control problem for a discrete system \jour Chelyab. Fiz.-Mat. Zh. \yr 2018 \vol 3 \issue 3 \pages 311--318 \mathnet{http://mi.mathnet.ru/chfmj107} \crossref{https://doi.org/10.24411/2500-0101-2018-13304} \elib{https://elibrary.ru/item.asp?id=35559234} 

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This publication is cited in the following articles:
1. S. A. Nikitina, V. I. Ukhobotov, “Diskretnaya lineinaya zadacha upravleniya s terminalnym mnozhestvom v forme koltsa pri nalichii pomekhi”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 102–107
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