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Computer Research and Modeling, 2024, Volume 16, Issue 2, Pages 299–314
DOI: https://doi.org/10.20537/2076-7633-2024-16-2-299-314
(Mi crm1163)
 

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Parametric identification of dynamic systems based on external interval estimates of phase variables

A. Yu. Morozova, D. L. Reviznikovab

a Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilov st., Moscow, 119333, Russia
b Moscow Aviation Institute (National Research University) (MAI), 4 Volokolamskoe highway, Moscow, 125993, Russia
References:
Abstract: An important role in the construction of mathematical models of dynamic systems is played by inverse problems, which in particular include the problem of parametric identification. Unlike classical models that operate with point values, interval models give upper and lower boundaries on the quantities under study. The paper considers an interpolation approach to solving interval problems of parametric identification of dynamic systems for the case when experimental data are represented by external interval estimates. The purpose of the proposed approach is to find such an interval estimate of the model parameters, in which the external interval estimate of the solution of the direct modeling problem would contain experimental data or minimize the deviation from them. The approach is based on the adaptive interpolation algorithm for modeling dynamic systems with interval uncertainties, which makes it possible to explicitly obtain the dependence of phase variables on system parameters. The task of minimizing the distance between the experimental data and the model solution in the space of interval boundaries of the model parameters is formulated. An expression for the gradient of the objectivet function is obtained. On a representative set of tasks, the effectiveness of the proposed approach is demonstrated.
Keywords: inverse problems, parametric identification, interval estimates, interval parameters, dynamical systems, ordinary differential equations, adaptive interpolation algorithm, gradient descent
Received: 22.11.2022
Revised: 16.02.2024
Accepted: 01.03.2024
Document Type: Article
UDC: 519.622.2 + 681.5.015
Language: Russian
Citation: A. Yu. Morozov, D. L. Reviznikov, “Parametric identification of dynamic systems based on external interval estimates of phase variables”, Computer Research and Modeling, 16:2 (2024), 299–314
Citation in format AMSBIB
\Bibitem{MorRev24}
\by A.~Yu.~Morozov, D.~L.~Reviznikov
\paper Parametric identification of dynamic systems based on external interval estimates of phase variables
\jour Computer Research and Modeling
\yr 2024
\vol 16
\issue 2
\pages 299--314
\mathnet{http://mi.mathnet.ru/crm1163}
\crossref{https://doi.org/10.20537/2076-7633-2024-16-2-299-314}
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