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Avtomat. i Telemekh., 2009, Issue 4, Pages 41–47 (Mi at449)  

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

Systems with Distributed Parameters

Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models

N. A. Sidorova, D. N. Sidorovb

a Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
b Melent'ev Institute of Power Engineering Systems, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

Abstract: Classes of nonlinear integral Volterra equations occurring in identifying dynamic systems are studied. A solution to a nonlinear system of integral Volterra equations of the first kind is constructed in the class of generalized functions with a point support in the form of a sum of singular and regular parts. In obtaining a singular part of the solution, a determined system of linear algebraic equations is used. The method of sequential approximations together with the method of undetermined coefficients allow constructing a regular part. Theorems of existence and uniqueness of generalized solutions are proved.

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English version:
Automation and Remote Control, 2009, 70:4, 598–604

Bibliographic databases:

PACS: 02.30.Rz, 02.30.Zz
Presented by the member of Editorial Board: . . 

Received: 01.10.2008

Citation: N. A. Sidorov, D. N. Sidorov, “Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models”, Avtomat. i Telemekh., 2009, no. 4, 41–47; Autom. Remote Control, 70:4 (2009), 598–604

Citation in format AMSBIB
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\by N.~A.~Sidorov, D.~N.~Sidorov
\paper Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models
\jour Avtomat. i Telemekh.
\yr 2009
\issue 4
\pages 41--47
\mathnet{http://mi.mathnet.ru/at449}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2536536}
\zmath{https://zbmath.org/?q=an:1181.93025}
\transl
\jour Autom. Remote Control
\yr 2009
\vol 70
\issue 4
\pages 598--604
\crossref{https://doi.org/10.1134/S0005117909040067}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65449138384}


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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. D. N. Sidorov, N. A. Sidorov, “Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials”, Autom. Remote Control, 72:6 (2011), 1258–1263  mathnet  crossref  mathscinet  zmath  isi
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