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

Abstract

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.

Recursive set-membership parameter estimation of fractional systems using orthotopic approach

“…In the literature, different forms have been proposed to approximate the feasible parameter set of integer models, such as ellipsoids (Belforte et al, 1990; Deller et al, 1994; Fogel and Huang, 1982), orthotopes (Cerone et al, 2011; Messaoud and Favier, 1993; Milanese and Belforte, 1982), zonotopes (Blesa et al, 2011; Bravo et al, 2006; Mo and Norton, 1990) and orthonormal basis functions (Casini et al, 2003). For fractional models, few studies have treated set-membership parameter estimation using an ellipsoidal approximation (Amairi, 2016) or a parallelotope approximation (Amairi et al, 2012). To improve the estimation algorithms of uncertain fractional systems for efficient applications in control (Saidi et al, 2015; Yakoub et al, 2017) and diagnosis, a new orthotopic approach has been developed recently (Hamdi et al, 2016).…”

An Interval Estimator for Chlorine Monitoring in Drinking Water Distribution Systems Under Uncertain System Dynamics, Inputs and Chlorine Concentration Measurement Errors

“…The process also includes modelling the uncertainty. There are several approaches to uncertainty modelling; however, a set-membership approach is an attractive option Amairi, 2016;Jauberthie et al, 2016). In this approach the uncertainty is described by means of an additive bounded error where only the bounds are known.…”