Parameter estimation of systems with delays via structural sensitivity analysis

Krzysztof Fujarewicz; Krzysztof Łakomiec

doi:10.3934/dcdsb.2014.19.2521

Article Contents

2014, Volume 19, Issue 8: 2521-2533. Doi: 10.3934/dcdsb.2014.19.2521

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Parameter estimation of systems with delays via structural sensitivity analysis

Krzysztof Fujarewicz^1, and
Krzysztof Łakomiec^1,

1.
Silesian University of Technology, ul.Akademicka 16, 44-100, Gliwice

Received: October 31, 2013

Revised: April 30, 2014

Published: September 2014

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Abstract

This article presents a method for sensitivity analysis of non-linear continuous-time models with delays and its application to parameter estimation. The method is universal and may be used for sensitivity analysis of any system given as a block diagram with arbitrary structure and any number of delays. The method gives sensitivity functions of model trajectories with respect to all model parameters, including delay times, and both forward and adjoint sensitivity analysis may be performed. Two examples application of the method are presented: identification of a Wiener model with delay and identification of a model of JAK-STAT cell signal transduction mechanism.

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Mathematics Subject Classification: Primary: 93B30, 93A30; Secondary: 65K10, 93C10.

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