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Trudy Mat. Inst. Steklova, 2015, Volume 291, Pages 231–243 (Mi tm3665)  

This article is cited in 3 scientific papers (total in 3 papers)

Calculation of the derivative of an inaccurately defined function by means of feedback laws

V. I. Maksimovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg, Russia

Abstract: The problem of calculating the derivative of an inaccurately defined function is considered. This problem is one of the “classical” problems in mathematical analysis. Various algorithms for solving this problem have been proposed by many authors. In the present study, constructions of positional control theory are invoked to solve this problem. Due to the presence of error in the measurement of the values of a function, the exact calculation of the derivative seems to be impossible. In view of this feature, a problem solving algorithm is presented that is based on an appropriate modification of the method of models controlled by feedback laws and is robust with respect to informational noise and measurement errors.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00110a
Ural Branch of the Russian Academy of Sciences 15-16-1-8
This work was supported by the Russian Foundation for Basic Research (project no. 13-01-00110a) and by the Ural Branch of the Russian Academy of Sciences within the program of support of fundamental research (project no. 15-16-1-8).


DOI: https://doi.org/10.1134/S0371968515040172

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 291, 219–231

Bibliographic databases:

UDC: 517.977
Received: November 15, 2014

Citation: V. I. Maksimov, “Calculation of the derivative of an inaccurately defined function by means of feedback laws”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 231–243; Proc. Steklov Inst. Math., 291 (2015), 219–231

Citation in format AMSBIB
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\by V.~I.~Maksimov
\paper Calculation of the derivative of an inaccurately defined function by means of feedback laws
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 231--243
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3665}
\crossref{https://doi.org/10.1134/S0371968515040172}
\elib{https://elibrary.ru/item.asp?id=24776674}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 219--231
\crossref{https://doi.org/10.1134/S0081543815080179}
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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. V. I. Maksimov, “On a control problem for a linear system with measurements of a part of phase coordinates”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 126–135  mathnet  crossref  crossref  isi  elib
    2. V. K. Maksimov, “Ob odnom algoritme rekonstruktsii vozmuscheniya nelineinoi sistemy”, Tr. IMM UrO RAN, 26, no. 1, 2020, 156–166  mathnet  crossref  elib
    3. P. G. Surkov, “Vychislenie v realnom vremeni drobnoi proizvodnoi Kaputo po zashumlennym dannym. Sluchai nepreryvnykh izmerenii”, Tr. IMM UrO RAN, 27, no. 2, 2021, 238–248  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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