Geodesic
Identification of linear dynamic systems of~fractional order with errors in variables based on~an~augmented system of equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 3, pp. 508-518

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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. 
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     author = {D. V. Ivanov},
     title = {Identification of linear dynamic systems of~fractional order with errors in variables based on~an~augmented system of equations},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {508--518},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2021_25_3_a6/}
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D. V. Ivanov. Identification of linear dynamic systems of~fractional order with errors in variables based on~an~augmented system of equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 3, pp. 508-518. http://geodesic.mathdoc.fr/item/VSGTU_2021_25_3_a6/