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 Chelyab. Fiz.-Mat. Zh., 2020, Volume 5, Issue 3, Pages 306–315 (Mi chfmj190)

Mathematics

On a problem of reserves control in the presence of an interference

S. A. Nikitina, V. I. Ukhobotov

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: An approach is proposed to solving the problem of reserves control in the discrete case. A controlled process whose duration is known is considered. The problem of retaining a phase point in a given family of sets at discrete time instants is solved. The case is considered when the control vectogram and the given family of sets are polyhedra defined using the system of linear inequalities. It is assumed that a certain linearity property is fulfilled for polyhedrals. An algorithm for constructing a control is written, which ensures the retention of the phase point in a given family of sets for any permissible implementation of the interference. In the practical part of the work, the application of the obtained results is shown by an example.

Keywords: discrete control problem, reserves control problem, polyhedral control set, retention problem.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00264_à The work is supported by the Russian Foundation for Basic Research, project 18-01-00264_à.

DOI: https://doi.org/10.47475/2500-0101-2020-15305

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UDC: 517.977
Revised: 17.08.2020

Citation: S. A. Nikitina, V. I. Ukhobotov, “On a problem of reserves control in the presence of an interference”, Chelyab. Fiz.-Mat. Zh., 5:3 (2020), 306–315

Citation in format AMSBIB
\Bibitem{NikUkh20} \by S.~A.~Nikitina, V.~I.~Ukhobotov \paper On a problem of reserves control in the presence of an interference \jour Chelyab. Fiz.-Mat. Zh. \yr 2020 \vol 5 \issue 3 \pages 306--315 \mathnet{http://mi.mathnet.ru/chfmj190} \crossref{https://doi.org/10.47475/2500-0101-2020-15305}