Parameter identification in classes of hereditary systems of neutral type
type: Item
instance of: scholarly article
title: Parameter identification in classes of hereditary systems of neutral type
zbMATH Open document ID: 0915.65077
DOI: 10.1016/S0096-3003(97)81654-2
author: Ferenc Hartung
author: Terry L. Herdman
author: Janos Turi
published in: Applied Mathematics and Computation
publication date: 1999-07-12T00:00:00Z
review text: The authors apply the general identification framework for identifying parameters in initial value problems corresponding to neutral functional differential equations (NFDEs) of the form \[ {d\over dt}(x(t)+ q(t)x(t- \tau(t)))= f(t,x(t), x(t-\sigma(t))),\quad t\in[0, T],\tag{1} \] and initial condition \[ x(t)=\varphi(t),\quad t\in[-r,0].\tag{2} \] The goal is the identification of \(q\), \(\tau\) in (1), and the associated initial function \(\varphi\) in (2). Assuming that the parameters \(q\), \(\tau\) and \(\varphi\) are continuous functions, the parameter space is the set \(\Gamma\equiv C([0,T]; \mathbb{R})\times C([0, T]; \mathbb{R})\times C([-r,0]; \mathbb{R}^n)\). To follow the general identification method, the authors first approximate \(q\), \(\tau\) and \(\varphi\) (in supremum norm) by (finite-dimensional) functions \(q^N\), \(\tau^N\) and \(\varphi^N\). In practice linear spline approximations are used. In Section 2, the authors define several Euler-type approximation schemes for NFDEs of the form (1), using equations with piecewise constant arguments, and show that each scheme satisfies the convergence property of the general method.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 1183193
zbMATH Keywords: hereditary system
zbMATH Keywords: parameter identifcation
zbMATH Keywords: neutral functional differential equations
zbMATH Keywords: linear spline approximations
zbMATH Keywords: Euler-type approximation
zbMATH Keywords: convergence
reviewed by: G. Dimitriu
MaRDI profile type: Publication
cites work: Parameter Estimation and Identification for Systems with Delays
cites work: Estimation techniques for distributed parameter systems
cites work: Estimation of Delays and Other Parameters in Nonlinear Functional Differential Equations
cites work: Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations
cites work: Q4100478
cites work: A difference equation approach to parameter estimation for differential- delay equations
cites work: The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods
cites work: On approximation of the solutions of delay differential equations by using piecewise constant arguments
cites work: Numerical approximations for a class of differential equations with time- and state-dependent delays
cites work: Introduction to functional differential equations
full work available at URL: s0096-3003(97)81654-2
OpenAlex ID: W2056470533
Recommended article: The stability of hereditary systems of neutral type
Recommended article: Identification of a hereditary system with distributed delay
Recommended article: Q3483161
Recommended article: Q4733738
Recommended article: Parameter identification of dynamical systems
Recommended article: On the equivalence of different classes of hereditary systems
Recommended article: Q4877688
Recommended article: Q4894705
Recommended article: Identifiability of parameter-dependent systems
Recommended article: Hereditary realizations of linear neutral delay-differential systems
description: scientific article; zbMATH DE number 1183193