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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 5, Pages 739–759
DOI: https://doi.org/10.31857/S004446692305006X
(Mi zvmmf11550)
 

This article is cited in 2 scientific papers (total in 2 papers)

Optimal control

Optimization of the reachable set of a linear system with respect to another set

M. V. Balashov, R. A. Kamalov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia
Citations (2)
Abstract: Given a linear controlled autonomous system, we consider the problem of including a convex compact set in the reachable set of the system in the minimum time and the problem of determining the maximum time when the reachable set can be included in a convex compact set. Additionally, the initial point and the time at which the extreme time is achieved in each problem are determined. Each problem is discretized on a grid of unit vectors and is then reduced to a linear programming problem to find an approximate solution of the original problem. Additionally, error estimates for the solution are found. The problems are united by a common ideology going back to the problem of finding the Chebyshev center.
Key words: reachable set, uniform convexity, condition of nonempty interior, multivalued integral, linear programming, approximation in the Hausdorff metric.
Funding agency Grant number
Russian Science Foundation 22-11-00042
The results in Sections 2, 3 were obtained by M.V. Balashov at the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, and his research was supported by the Russian Science Foundation, grant no. 22-11-00042, https://rscf.ru/en/project/22-11-00042/.
Received: 02.11.2022
Revised: 21.11.2022
Accepted: 02.02.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 5, Pages 751–770
DOI: https://doi.org/10.1134/S0965542523050056
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: M. V. Balashov, R. A. Kamalov, “Optimization of the reachable set of a linear system with respect to another set”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 739–759; Comput. Math. Math. Phys., 63:5 (2023), 751–770
Citation in format AMSBIB
\Bibitem{BalKam23}
\by M.~V.~Balashov, R.~A.~Kamalov
\paper Optimization of the reachable set of a linear system with respect to another set
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 5
\pages 739--759
\mathnet{http://mi.mathnet.ru/zvmmf11550}
\crossref{https://doi.org/10.31857/S004446692305006X}
\elib{https://elibrary.ru/item.asp?id=53738567}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 5
\pages 751--770
\crossref{https://doi.org/10.1134/S0965542523050056}
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  • https://www.mathnet.ru/eng/zvmmf/v63/i5/p739
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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