Identification and observer synthesis of nonlinear systems using Laguerre multiple models

This paper proposes a new nonlinear model entitled decoupled state Laguerre multiple models approach used for modeling nonlinear systems. This representation is a combination between the classical multiple models approach and the Laguerre orthogonal bases used for modeling the sub-systems. The goal of this combination is to reduce the complexity of the identification algorithm of multiple models approach and to make a parametric reduction. The resulting multiple models prods with its parameter complexity reduction and with its simple structure offers the possibility to applying online identification algorithms and, therefore, the synthesis of adaptive control algorithms. The parameter identification of the Laguerre multiple models is achieved by using the Newton-Raphson algorithm. The performances of the Laguerre multiple models and the proposed identification approach are illustrated by numerical simulations.