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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 3, Pages 265–278
DOI: https://doi.org/10.21538/0134-4889-2019-25-3-265-278 (Mi timm1663) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On a control problem under a disturbance and a possible breakdown

V. I. Ukhobotov

Chelyabinsk State University
Full-text PDF (228 kB) Citations (6)
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DOI: https://doi.org/10.21538/0134-4889-2019-25-3-265-278
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.
Keywords: control, disturbance, breakdown.
Funding agency Grant number
Russian Science Foundation 19-11-00105
This work was supported by the Russian Science Foundation (project no. 19-11-00105).
Received: 21.05.2019
Revised: 01.07.2019
Accepted: 08.07.2019
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, Volume 307, Issue 1, Pages S159–S171
DOI: https://doi.org/10.1134/S0081543819070137
Bibliographic databases:
Document Type: Article
UDC: 519.857
MSC: 91A23, 91A24, 91A80
Language: Russian
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
Citation in format AMSBIB
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\paper On a control problem under a disturbance and a possible breakdown
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\vol 25
\issue 3
\pages 265--278
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    • This publication is cited in the following 6 articles:
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