Partially-Linear Least-Squares Regularized Regression for System Identification

In this technical note, we propose a partially-linear least-squares regularized regression (PL-LSRR) method for system identification. This method identifies a general nonlinear function as a sum of two functions which come from a linear and a nonlinear function space respectively. Both the linear and nonlinear functions can involve all regressors. Therefore, the PL-LSRR can make use of the partially-linear structure of a given system to reduce prediction errors more efficiently than exiting partially-linear identification methods. Two examples show that the PL-LSRR can reduce prediction errors and estimate the true linear expansion of the system well.