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Mat. Zametki, 2010, Volume 87, Issue 3, Pages 337–358 (Mi mz7837)  

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

On the Guaranteed Accuracy of a Dynamical Recovery Procedure for Controls with Bounded Variation in Systems Depending Linearly on the Control

A. Yu. Vdovin, S. S. Rubleva

Ural State Forest Engineering University

Abstract: We obtain an upper bound for the accuracy of a modification of the finite-step dynamical reconstruction algorithm proposed by Yu. S. Osipov and A. V. Kryazhimskii for the unknown control in the dynamical system from inaccurate data on its trajectory We establish that, for the case in which the control is a function of bounded variation and the subspace of the image of the matrix of its coefficients has constant dimension, the asymptotic order in the metric of the space $L_1[a,b]$ of its accuracy with respect to the input error is $1/2$.

Keywords: dynamical system, dynamical reconstruction algorithm, admissible control, Tikhonov functional, Cauchy problem, dichotomy, Euler method

DOI: https://doi.org/10.4213/mzm7837

Full text: PDF file (584 kB)
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English version:
Mathematical Notes, 2010, 87:3, 316–335

Bibliographic databases:

Document Type: Article
UDC: 517.938+519.65
Received: 29.01.2009
Revised: 03.07.2009

Citation: A. Yu. Vdovin, S. S. Rubleva, “On the Guaranteed Accuracy of a Dynamical Recovery Procedure for Controls with Bounded Variation in Systems Depending Linearly on the Control”, Mat. Zametki, 87:3 (2010), 337–358; Math. Notes, 87:3 (2010), 316–335

Citation in format AMSBIB
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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. Vdovin A.Yu., Rubleva S.S., “Ob otsenke tochnosti dinamicheskogo algoritma vosstanovleniya upravleniya na beskonechnom vremennom promezhutke”, Sovremennye problemy nauki i obrazovaniya, 2012, no. 6, 588–588  elib
  • Математические заметки Mathematical Notes
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