Least squares support vector machine based partially linear model identification

Abstract

A nonlinear identification method was proposed for a class of partially linear models (PLM) which consist of a linear component summed with a nonlinear component in nonlinear ARX form. The method extends the standard least squares support vector machine (LSSVM) by replacing the equality constraint in the standard LSSVM with a PLM model. To guarantee the uniqueness of the linear coefficients, we imposed an additional explicit constraint on the feature map instead of an implicit constraint on the regressor vectors. Therefore the resulting PLM is a generalized version of the original one. Two examples show the effectiveness of the presented method. © Springer-Verlag Berlin Heidelberg 2006.