International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 2016
Volume 26 - 2016

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

Carine Jauberthie, Louise Travé-Massuyès, Nathalie Verdière

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.

identifiability, bounded uncertainty, set-membership estimation, nonlinear dynamic models