Identification of Wiener-Hammerstein systems by ℓ1–constrained Volterra series

Abstract In the paper the Wiener–Hammerstein (LNL) system is identified with the help of Volterra series and l 1 -constrained least squares. The nonparametric approach to the problem ensures wide applicability of the proposed method, as it does not require an extensive a priori knowledge about the underlying system. In the main part of the paper, the convergence of the identification algorithm is shown for a general class of systems with smooth nonlinearities and stable dynamics, under the assumption that the input is a bounded i.i.d.random signal. The rate of convergence is examined as well. Moreover, the large error of the standard least squares-based models, inherently associated with high dimensional representations (such as those based on Volterra series expansion), is reduced by the imposed l 1 -constraint and hence the method allows for a scarcer data set. In addition, the results of numerical simulations are provided to illustrate the superiority of the proposed method over the standard one.