Recursive identification of block-oriented nonlinear systems in the presence of outliers

Abstract

The paper considers the recursive identification of nonlinear (Hammerstein) model in the presence of outliers. In this model the nonlinear part is a polynomial of a known order in the input and linear part is described as an ARX (auto - regressive model with exogenous inputs) model. It is assumed that there is a priori information about a disturbance distribution in the form of a class of distributions. Owing that fact it is possible to use robust statistics in the sense of Huber. But Huber`s loss function is only first order differentiable. It follows that second order methods (Newton – Raphson methodology) cannot be used. The problem is avoided by analysis of the structure of least favourable distribution. It is shown that robust recursive algorithm derivation can be set in frame of l1−l2 – norm estimation problem. The main contributions of the paper are: (i) it is shown that the robust identification belongs to l1−l2 – norm estimation problem; (ii) the derivation of the new robust recursive algorithm; (iii) it is shown that robust recursive algorithm is switching algorithm (collection of linear least squares and sign algorithm) and that fact opens the new research opportunities.