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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2021, Volume 25, Number 3, Pages 508–518 (Mi vsgtu1854)  

Mathematical Modeling, Numerical Methods and Software Complexes

Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

D. V. Ivanov

Samara State Transport University, Samara, 443066, Russian Federation

Abstract: Equations with derivatives and fractional order differences are widely used to describe various processes and phenomena. Currently, methods of identification of systems described by equations with fractional order differences are actively developing. The paper is devoted to the identification of discrete dynamical systems described by equations with fractional order differences with errors in variables. The problems of identifying systems with errors in variables are often ill-conditioned. The paper proposes an algorithm that uses the representation of a normal biased system as an augmented equivalent system. This representation allows to reduce the number of conditionality of the problem to be solved. Test examples have shown that the proposed algorithm has a higher accuracy than the algorithms based on the decomposition of Cholesky and the minimization of the generalized Rayleigh quotient.

Keywords: fractional difference, total least square, errors-in-variables, ill-conditioning

DOI: https://doi.org/10.14498/vsgtu1854

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Bibliographic databases:

UDC: 519.254
MSC: 93E12, 15A29
Received: March 20, 2021
Revised: June 24, 2021
Accepted: June 28, 2021
First online: September 27, 2021
Language:

Citation: D. V. Ivanov, “Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:3 (2021), 508–518

Citation in format AMSBIB
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\by D.~V.~Ivanov
\paper Identification of linear dynamic systems of~fractional order with errors in variables based on~an~augmented system of equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 3
\pages 508--518
\mathnet{http://mi.mathnet.ru/vsgtu1854}
\crossref{https://doi.org/10.14498/vsgtu1854}
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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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