Set membership estimation of fractional models in the frequency domain

Abstract

The main objective of this paper is to estimate the whole set of feasible parameters of a fractional differentiation model, based on gain and phase frequency data. All parameters, including differentiation orders, are expressed as intervals and then estimated using a bounded error approach. A contraction method named forward-backward propagation is first applied to reduce the initial searching space. Then, a set inversion algorithm named SIVIA is applied on the reduced searching space to obtain the whole set of feasible parameters. One of the interesting points of this study is to show the separate contribution of gain and phase data on the final estimation.