Making parametric Hammerstein system identification a linear problem

Abstract

AbstractIn this paper, we study identification of parametric Hammerstein systems with FIR linear parts. By a proper normalization and a clever characterization, it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate. Further the cost function is concave in the inner product and linear in the inner product square. Therefore, identification of parametric Hammerstein systems with FIR linear parts is a globally convergent problem and has one and only one (local and global) minimum. This implies that identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally.