Set-membership identifiability of nonlinear models and related parameter estimation properties

Carine Jauberthie; Louise Travé-Massuyès; Nathalie Verdière

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 4, page 803-813
  • ISSN: 1641-876X

Abstract

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Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

How to cite

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Carine Jauberthie, Louise Travé-Massuyès, and Nathalie Verdière. "Set-membership identifiability of nonlinear models and related parameter estimation properties." International Journal of Applied Mathematics and Computer Science 26.4 (2016): 803-813. <http://eudml.org/doc/287180>.

@article{CarineJauberthie2016,
abstract = {Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.},
author = {Carine Jauberthie, Louise Travé-Massuyès, Nathalie Verdière},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {identifiability; bounded uncertainty; set-membership estimation; nonlinear dynamic models},
language = {eng},
number = {4},
pages = {803-813},
title = {Set-membership identifiability of nonlinear models and related parameter estimation properties},
url = {http://eudml.org/doc/287180},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Carine Jauberthie
AU - Louise Travé-Massuyès
AU - Nathalie Verdière
TI - Set-membership identifiability of nonlinear models and related parameter estimation properties
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 4
SP - 803
EP - 813
AB - Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.
LA - eng
KW - identifiability; bounded uncertainty; set-membership estimation; nonlinear dynamic models
UR - http://eudml.org/doc/287180
ER -

References

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