Incorporating Term selection into nonlinear block structured system identification

Subset selection and shrinkage methods locate and remove insignificant terms from identified models. The least absolute shrinkage and selection operator (Lasso) is a term selection method that shrinks some coefficients and sets others to zero. In this paper, the incorporation of constraints (such as Lasso) into the linear and/or nonlinear parts of a Separable Nonlinear Least Squares algorithm is addressed and its application to the identification of block-structured models is considered. As an example, this method is applied to a Hammerstein model consisting of a nonlinear static block, represented by a Tchebyshev polynomial, in series with a linear dynamic system, modeled by a bank of Laguerre filters. Simulations showed that the Lasso based method was able to identify the model structure correctly, or with mild over-modeling, even in the presence of significant output noise.