A new multimodel approach by Laguerre filters on sliding window for nonlinear system identification and control

This paper proposes an online identification procedure on sliding window with the synthesis of a nonlinear adaptive predictive control for a new nonlinear model resulting in multimodel approach. Such a model is entitled ARX-Laguerre multimodel obtained by expanding the conventional ARX multimodel on independent Laguerre orthonormal bases. It allows a significant parameter number reduction as well as a simple recursive representation compared with the ARX-multimodel. This parametric reduction is provided from an optimal iteratif identification approach of the Laguerre poles presented in Adaily et al. (2013). We propose to combine and carry out this identification approach on a sliding window to achieve an online identification procedure of the ARX-Laguerre multimodel for real time procedure depending on Fourier coefficients that are identified by a regularized square error. This property allows to synthese a new nonlinear adaptive predictive control on sliding window. We develop the general form of a new predictor and so, we propose an optimization algorithm formulated as a quadratic programming (QP) under linear constraints for an adaptive control law. The performances of the proposed online identification procedure and the developed nonlinear adaptive control algorithm are illustrated on a benchmark system as the continuous stirred tank reactor system (CSTR) with respect to the process parameter uncertainties.