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

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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.

About the authors

Dmitriy V. Ivanov

Samara State Transport University

Author for correspondence.
Email: dvi85@list.ru
ORCID iD: 0000-0002-5021-5259
SPIN-code: 6672-4830
Scopus Author ID: 22937879800
ResearcherId: C-9460-2018
http://www.mathnet.ru/person42123

Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Mechatronics, Automation, and Transport Control

2 V, Svobody st., Samara, 443066, Russian Federation

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