Identification of nonlinear systems by the new representation ARX-Laguerre decoupled multimodel

This paper proposes a new alternative in the multimodel approach by expanding each ARX sub-model on independent orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting multimodel, entitled ARX-Laguerre decoupled multimodel, ensures the parameter number reduction with a recursive and easy representation. However, such reduction is still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al. [17]. The ARX-Laguerre decoupled multimodel as well as the proposed pole optimization algorithm are illustrated and validated on a numerical simulation.