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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 1, Pages 74–81 (Mi vuu621)  

This article is cited in 4 scientific papers (total in 4 papers)


Dynamic control problem under interference with a given set of correction momenta

V. I. Ukhobotov, I. S. Stabulit

Chelyabinsk State University, ul. Brat'ev Kashirinykh, 129, Chelyabinsk, 454001, Russia

Abstract: We consider a dynamic control system under interference. A set of correction momenta of the controls is given. The problem of phase point retention in a given collection of sets at correction momenta is considered. Instantaneous change of a position is admissible. Necessary and sufficient conditions for the possibility of retention are found. As an example, we consider a discrete linear control problem under interference and with the one-dimensional aim. The condition of one-dimensionality of the aim means that the modulus of the value of a given linear function of the phase variables at a fixed moment of the control process end should not be more than a given number. For this problem, necessary and sufficient conditions are found in an explicit form, the fulfillment of which guarantees the existence of an admissible control that ensures the achievement of the aim for any admissible realization of the interference. This control is constructed in an explicit form, and information about the realized value of the interference is not used. We constructed the interference which guarantees that the aim will not be reached at any admissible control from the initial state that does not satisfy the obtained conditions.

Keywords: control, interference, correction.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00264_а


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Bibliographic databases:

UDC: 517.977
MSC: 91A23, 49N75
Received: 28.12.2017

Citation: V. I. Ukhobotov, I. S. Stabulit, “Dynamic control problem under interference with a given set of correction momenta”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 74–81

Citation in format AMSBIB
\by V.~I.~Ukhobotov, I.~S.~Stabulit
\paper Dynamic control problem under interference with a given set of correction momenta
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 74--81

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    This publication is cited in the following articles:
    1. S. A. Nikitina, A. S. Skorynin, V. I. Ukhobotov, “Ob odnoi zadache upravleniya diskretnoi sistemoi”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 311–318  mathnet  crossref  elib
    2. V. I. Ukhobotov, S. A. Nikitina, “Upravlenie diskretnoi dinamicheskoi sistemoi s pomekhoi”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 168, VINITI RAN, M., 2019, 105–113  mathnet  crossref
    3. I. V. Izmestev, “Diskretnaya igrovaya zadacha s terminalnym mnozhestvom v forme koltsa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 18–30  mathnet  crossref
    4. 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
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