Estimation of initial functions for systems with delays from discrete measurements

The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assume...

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Main Author: Krzysztof Fujarewicz
Format: Article
Language:English
Published: AIMS Press 2017-01-01
Series:Mathematical Biosciences and Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2017011
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author Krzysztof Fujarewicz
author_facet Krzysztof Fujarewicz
author_sort Krzysztof Fujarewicz
collection DOAJ
description The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assumed that the system is continuous-time and described by ordinary differential equations with delays but the estimation is done based on discrete-time measurements of the signals appearing in the system. Results of gradient-based estimation of initial functions for exemplary models are presented and discussed.
format Article
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institution Kabale University
issn 1551-0018
language English
publishDate 2017-01-01
publisher AIMS Press
record_format Article
series Mathematical Biosciences and Engineering
spelling doaj-art-a6fd8f8551ef4a2498754c98ab5ced0a2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114116517810.3934/mbe.2017011Estimation of initial functions for systems with delays from discrete measurementsKrzysztof Fujarewicz0Silesian University of Technology, Akademicka 16, 44-100 Gliwice, PolandThe work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assumed that the system is continuous-time and described by ordinary differential equations with delays but the estimation is done based on discrete-time measurements of the signals appearing in the system. Results of gradient-based estimation of initial functions for exemplary models are presented and discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2017011delay differential equationssystems with delaysinitial functionsparameter estimationadjoint sensitivity analysissampled systems
spellingShingle Krzysztof Fujarewicz
Estimation of initial functions for systems with delays from discrete measurements
Mathematical Biosciences and Engineering
delay differential equations
systems with delays
initial functions
parameter estimation
adjoint sensitivity analysis
sampled systems
title Estimation of initial functions for systems with delays from discrete measurements
title_full Estimation of initial functions for systems with delays from discrete measurements
title_fullStr Estimation of initial functions for systems with delays from discrete measurements
title_full_unstemmed Estimation of initial functions for systems with delays from discrete measurements
title_short Estimation of initial functions for systems with delays from discrete measurements
title_sort estimation of initial functions for systems with delays from discrete measurements
topic delay differential equations
systems with delays
initial functions
parameter estimation
adjoint sensitivity analysis
sampled systems
url https://www.aimspress.com/article/doi/10.3934/mbe.2017011
work_keys_str_mv AT krzysztoffujarewicz estimationofinitialfunctionsforsystemswithdelaysfromdiscretemeasurements