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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2019, Volume 25, Issue 4, Pages 36–47 (Mi vsgu618)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Problems of differential and topological diagnostics. Part 3. The checking problem

M. V. Shamolin

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119192, Russian Federation

Abstract: Proposed work is the third in the cycle, therefore, we explain such notions as checking sphere, checking ellipsoid and checking tubes. The checking problem is stated and the algorithms for solving it are formulated. The criterion for a malfunction in a controlled system whose motion is described by ordinary differential equations is taken to be the attainment of a checking surface by the checking vector. We first propose the methods for solving the checking problems in which the checking surfaces are chosen in the form of a checking sphere, checking ellipsoid or checking tube. Then we consider the general techniques for constructing the checking surface by using the statistical testing method. We also give the extended statement of the checking problem. And we also prepare the material for the consideration of the problem of diagnostics.

Keywords: checking sphere, checking ellipsoid, checking tubes, extended statement of the checking problem.

DOI: https://doi.org/10.18287/2541-7525-2019-25-4-36-47

Full text: PDF file (230 kB)
Full text: https:/.../7920 (published under the terms of the Creative Commons Attribution 4.0 International License)
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UDC: 517+531.01
Received: 10.10.2019
Accepted:24.10.2019

Citation: M. V. Shamolin, “Problems of differential and topological diagnostics. Part 3. The checking problem”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 25:4 (2019), 36–47

Citation in format AMSBIB
\Bibitem{Sha19}
\by M.~V.~Shamolin
\paper Problems of differential and topological diagnostics. Part~3. The checking problem
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2019
\vol 25
\issue 4
\pages 36--47
\mathnet{http://mi.mathnet.ru/vsgu618}
\crossref{https://doi.org/10.18287/2541-7525-2019-25-4-36-47}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Shamolin, “Zadachi differentsialnoi i topologicheskoi diagnostiki. Chast 4. Zadacha diagnostirovaniya (sluchai tochnykh traektornykh izmerenii)”, Vestn. SamU. Estestvennonauchn. ser., 26:1 (2020), 52–68  mathnet  crossref
  • Вестник Самарского государственного университета. Естественнонаучная серия
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