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.
@article{bwmeta1.element.bwnjournal-article-amcv26i4p803bwm,
author = {Carine Jauberthie and Louise Trav\'e-Massuy\`es and Nathalie Verdi\`ere},
title = {Set-membership identifiability of nonlinear models and related parameter estimation properties},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {26},
year = {2016},
pages = {803-813},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv26i4p803bwm}
}
Carine Jauberthie; Louise Travé-Massuyès; Nathalie Verdière. Set-membership identifiability of nonlinear models and related parameter estimation properties. International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) pp. 803-813. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv26i4p803bwm/
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