Internal Estimation of the Information Set of an Interval Data Based Parametric Identification Problem for Dynamical Systems

We consider the method of internal interval estimation of the information set in the parametric identification problem for dynamical systems, where the experimental data are specified in the form of intervals. The state of the dynamical systems under consideration at each time is a parametric set. T...

Full description

Saved in:
Bibliographic Details
Published in:Differential equations Vol. 61; no. 7; pp. 1150 - 1162
Main Authors: Morozov, A. Yu, Reviznikov, D. L.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.07.2025
Subjects:
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
inverse problem
parametric identification
interval estimate
interval parameter
ordinary differential equation
gradient
adaptive interpolation algorithm
information set
dynamical system
objective function
ISSN:0012-2661, 1608-3083
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the method of internal interval estimation of the information set in the parametric identification problem for dynamical systems, where the experimental data are specified in the form of intervals. The state of the dynamical systems under consideration at each time is a parametric set. The objective function is constructed in the space of interval estimates of parameters, characterizing the degree of inclusion of parametric sets of states in the specified experimental interval estimates of the state variables. An expression for the gradient of the objective function is obtained. The proposed approach consists of two stages. At the first stage, the objective function is minimized by first-order optimization methods, and at the second stage, the resulting estimate of the information set is successively expanded with control of the objective function value. To solve a variety of direct problems when constructing the desired estimate, the adaptive interpolation algorithm previously developed by the authors is used. The efficiency and performance of the approach under consideration is demonstrated on a representative series of problems.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266125070109