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.
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
\Bibitem{UkhSta18}
\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
\mathnet{http://mi.mathnet.ru/vuu621}
\crossref{https://doi.org/10.20537/vm180107}
\elib{https://elibrary.ru/item.asp?id=32697217}
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https://www.mathnet.ru/eng/vuu/v28/i1/p74
This publication is cited in the following 8 articles:
S. A. Nikitina, V. I. Ukhobotov, “Discrete Linear Control Problem with the Ring-Shaped Terminal Set in the Presence of Noise”, J Math Sci, 2024
V. I. Ukhobotov, S. A. Nikitina, “Control of a Discrete Dynamical System with Noise”, J Math Sci, 262:6 (2022), 869
I. V. Izmestev, V. I. Ukhobotov, “Ob odnoi diskretnoi igrovoi zadache s nevypuklymi vektogrammami upravlenii”, Izv. IMI UdGU, 58 (2021), 48–58
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
S. A. Nikitina, V. I. Ukhobotov, “Ob odnoi zadache upravleniya zapasami pri nalichii pomekhi”, Chelyab. fiz.-matem. zhurn., 5:3 (2020), 306–315
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. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 102–107
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. Sovrem. mat. i ee pril. Temat. obz., 168, VINITI RAN, M., 2019, 105–113
S. A. Nikitina, A. S. Skorynin, V. I. Ukhobotov, “Ob odnoi zadache upravleniya diskretnoi sistemoi”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 311–318
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