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2 International Journal of Applied Mathematics and Computer Science

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

Jauberthie C., Travé-Massuyès L., Verdière N.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 4

803--813

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.

Set membership estimation of parameters and variables in dynamic networks by recursive algorithms with a moving measurement window

Duzinkiewicz K.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 2

209-217

The paper considers a set membership joint estimation of variables and parameters in complex dynamic networks based on parametric uncertain models and limited hard measurements. A recursive estimation algorithm with a moving measurement window is derived that is suitable for on-line network monitoring. The window allows stabilising the classic recursive estimation algorithm and significantly improves estimate tightness. The estimator is validated on a case study regarding a water distribution network. Tight set estimates of unmeasured pipe flows, nodal heads, tank level and pipe resistances are obtained.