Abstract:
A linear control problem is considered in the presence of an uncontrolled disturbance. It is only known that the values of the disturbance belong to a given connected compact set. The terminal time of the control process is fixed. The terminal component of the payoff depends on the modulus of a linear function of the phase variables, and the integral component is given by an integral of a power of the control. We admit the possibility of one breakdown leading to a change in the dynamics of the control process. The time of the breakdown is not known in advance. The construction of the control is based on the principle of minimizing the guaranteed result. The opponents are the disturbance and the time of the breakdown. Necessary and sufficient conditions for the optimality of an admissible control are found.
Citation:
V. I. Ukhobotov, “On a control problem under a disturbance and a possible breakdown”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 265–278; Proc. Steklov Inst. Math. (Suppl.), 307, suppl. 1 (2019), S159–S171
\Bibitem{Ukh19}
\by V.~I.~Ukhobotov
\paper On a control problem under a disturbance and a possible breakdown
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 3
\pages 265--278
\mathnet{http://mi.mathnet.ru/timm1663}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-3-265-278}
\elib{https://elibrary.ru/item.asp?id=39323553}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 307
\issue , suppl. 1
\pages S159--S171
\crossref{https://doi.org/10.1134/S0081543819070137}
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Linking options:
https://www.mathnet.ru/eng/timm1663
https://www.mathnet.ru/eng/timm/v25/i3/p265
This publication is cited in the following 7 articles:
N. N. Petrov, E. S. Fomina, “A problem of simple group pursuit with possible dynamical disturbance in dynamics and phase constraints”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 35:1 (2025), 82–95
I. V. Izmestev, N. D. Livanov, “Zadacha upravleniya parabolicheskoi sistemoi s pomekhami i vozmozhnymi izmeneniyami v dinamike”, Izv. IMI UdGU, 64 (2024), 34–47
I. V. Izmestev, V. I. Ukhobotov, “Zadacha upravleniya parabolicheskoi sistemoi s pomekhami i vypukloi tselyu”, Izv. IMI UdGU, 62 (2023), 30–42
A. A. Mel'nikova, P. A. Tochilin, “On a Problem of Calculating the Solvability Set for a Linear System with Uncertainty”, Differentsialnye uravneniya, 59:11 (2023), 1533
V. N. Ushakov, V. I. Ukhobotov, I. V. Izmestyev, “On a Problem of Impulse Control under Disturbance and Possible Breakdown”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S236–S249
M. I. Gomoyunov, D. A. Serkov, “On guarantee optimization in control problem with finite set of disturbances”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:4 (2021), 613–628
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
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