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Article information
2020 , Volume 25, ¹ 3, p.66-76
Lomov A.A.
Parameter identification of discrete stochastic systems by the inverse iteration method
The article addresses the problem of identifying parameters of discrete stochastic systems with perturbations in the residual of the equation and observation of variables. The identification functional in the problem has a complex nature of isosurfaces, which is why universal minimization algorithms based on estimates of the first and second derivatives have a small radius of convergence.It is proposed to employ efficient computational identification algorithms with inverse iterations in a variable metric for solving the convergence problem for two classes of systems with simple correspondence between matrix elements and parameters of equivalent systems without state variables. These algorithms are used for systems without state variables due to the large radius and high convergence rate since the 1970s. At first, a theorem on the conditions for convergence of inverse iterations from almost any initial approximation to a small neighborhood of the global minimum of the identification functional was proved. Secondly, a theorem on the convergence of the points of the global minimum of the identification functional to the desired true value with an increase in the sample size of observations is taken into account. Assumption of a zero first and restricted second moments of stochastic disturbances in the residual of the equation and observation of variables was made. The convergence of inverse iterations is shown numerically in a model example with significant values of disturbances. The result of the article is new theorems on the conditions of global convergence of computational algorithms with inverse iterations in the problem with mixed disturbances and the justification of possibility of using these algorithms to identify the parameters for discrete stochastic systems of two classes with a simple correspondence between matrix elements and parameters of equivalent systems without state variables
[full text] [link to elibrary.ru]
Keywords: discrete stochastic systems, parameter identification, inverse iterations, consistency
doi: 10.25743/ICT.2020.25.3.008
Author(s):
Lomov Andrei Aleksandrovich
Dr. , Associate Professor
Position: Senior Research Scientist
Office: Sobolev Institute of Mathematics, Novosibirsk State University
Address: 630090, Russia, Novosibirsk
Phone Office: (383) 329 7558
E-mail: lomov@math.nsc.ru
SPIN-code: 7357-8545 References:
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Bibliography link:
Lomov A.A. Parameter identification of discrete stochastic systems by the inverse iteration method // Computational technologies. 2020. V. 25. ¹ 3. P. 66-76
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