Support kernels regression for NARMA system identification (SKR<SUB align="right">NARMA)

Abstract

This paper deals with the identification of nonlinear systems using multi-kernel approach. First, we have improved the support vector regression (SVR) method in order to identify nonlinear complex system. Our idea consists of dividing the regressor vector in several blocks, and, for each one a kernel function is used. This blockwise SVR approach is called support kernel regression (SKR). Furthermore, we have proposed two methods, SKR(rbf-lin) and SKR(rbf-rbf). Second, the SKR approach is improved to deal with the problem of NARMA system identification. Therefore, a new method called support kernel regression for NARMA model (SKRNARMA) is suggested. The basic idea is to consider the terms of auto-correlation and cross-correlation of the nonlinearity of input output discrete time processes, and for every term a kernel function is used. An example of MIMO system is presented for qualitative comparison with the classical SVR approach based on a single kernel function. The results reveal the accuracy and the robustness of the obtained model based on our proposed (SKRNARMA)-based approach.