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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.

Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors

Amairi M.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 3

543--553

This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

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.