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

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.

Stochastic Convergence of Optimal Bounding Ellipsoid Algorithms

Given appropriate persistency of excitation, the ellipsoidal seta associated with optimal bounding ellipsoid (OBE) algorithms with an interpretable optimization (volume) criterion, converge to a point under the condition that the model disturbance process visit the error bounds infinitely often. The spectral properties of the disturbance are not primary in the convergence behavior of OBE algorithms, rendering these identifiers distinctly different from the structurally similar RLS. Rigorous proof of the sufficiency of the "infinite visitation" property is given for both independent and correlated noise. In the colored noise case, it is shown that a mixing condition on the observations will assure convergence if the OBE algorithm is slightly modified. Examples of simulations are used to illustrate the theoretical developments.