Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions

Gergely Szlobodnyik; Gábor Szederkényi

Kybernetika (2021)

  • Volume: 57, Issue: 6, page 939-957
  • ISSN: 0023-5954

Abstract

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In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain representations of the Volterra kernels, i. e. the Generalized Frequency Response Functions (GFRFs), in order to test the unique computability of the parameters. The advantage of representing nonlinear systems with their GFRFs is that in the frequency domain representation the time delay parameters appear explicitly in the exponents of complex exponential functions from which they can be easily extracted. Since the GFRFs can be symmetrized to be unique, they provide us with an exhaustive summary of the underlying model structure. We use the GFRFs to derive equations for testing structural identifiability. Unique solution of the composed equations with respect to the parameters provides sufficient conditions for structural identifiability. Our method is illustrated on non-linear dynamical system models of different degrees of non-linearities and multiple time delayed terms. Since Volterra series representation can be applied for input-output models, it is also shown that after differential algebraic elimination of unobserved state variables, the proposed method can be suitable for identifiability analysis of a more general class of non-linear time delayed state space models.

How to cite

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Szlobodnyik, Gergely, and Szederkényi, Gábor. "Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions." Kybernetika 57.6 (2021): 939-957. <http://eudml.org/doc/297581>.

@article{Szlobodnyik2021,
abstract = {In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain representations of the Volterra kernels, i. e. the Generalized Frequency Response Functions (GFRFs), in order to test the unique computability of the parameters. The advantage of representing nonlinear systems with their GFRFs is that in the frequency domain representation the time delay parameters appear explicitly in the exponents of complex exponential functions from which they can be easily extracted. Since the GFRFs can be symmetrized to be unique, they provide us with an exhaustive summary of the underlying model structure. We use the GFRFs to derive equations for testing structural identifiability. Unique solution of the composed equations with respect to the parameters provides sufficient conditions for structural identifiability. Our method is illustrated on non-linear dynamical system models of different degrees of non-linearities and multiple time delayed terms. Since Volterra series representation can be applied for input-output models, it is also shown that after differential algebraic elimination of unobserved state variables, the proposed method can be suitable for identifiability analysis of a more general class of non-linear time delayed state space models.},
author = {Szlobodnyik, Gergely, Szederkényi, Gábor},
journal = {Kybernetika},
keywords = {structural identifiability; Volterra series; generalized frequency response},
language = {eng},
number = {6},
pages = {939-957},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions},
url = {http://eudml.org/doc/297581},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Szlobodnyik, Gergely
AU - Szederkényi, Gábor
TI - Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 6
SP - 939
EP - 957
AB - In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain representations of the Volterra kernels, i. e. the Generalized Frequency Response Functions (GFRFs), in order to test the unique computability of the parameters. The advantage of representing nonlinear systems with their GFRFs is that in the frequency domain representation the time delay parameters appear explicitly in the exponents of complex exponential functions from which they can be easily extracted. Since the GFRFs can be symmetrized to be unique, they provide us with an exhaustive summary of the underlying model structure. We use the GFRFs to derive equations for testing structural identifiability. Unique solution of the composed equations with respect to the parameters provides sufficient conditions for structural identifiability. Our method is illustrated on non-linear dynamical system models of different degrees of non-linearities and multiple time delayed terms. Since Volterra series representation can be applied for input-output models, it is also shown that after differential algebraic elimination of unobserved state variables, the proposed method can be suitable for identifiability analysis of a more general class of non-linear time delayed state space models.
LA - eng
KW - structural identifiability; Volterra series; generalized frequency response
UR - http://eudml.org/doc/297581
ER -

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