Optimal expansions of discrete-time bilinear models using Laguerre functions

In this paper, we propose a new reduced complexity model by expanding discrete-time bilinear model on Laguerre orthonormal bases. Thus the coefficients associated to the input, to the output and to the crossed product of the bilinear model are expanded on three independent Laguerre bases. The resulting model is entitled bilinear-Laguerre model with filters on model input and output. The parametric complexity reduction of the proposed model with respect to the classical bilinear model is proved theoretically. The structure and the parameter identification of the bilinear-Laguerre model is achieved by a new proposed approach which consists in solving an optimization problem built from the bilinear model without using system input/output observations. The performances of the proposed bilinear-Laguerre model and the proposed identification approach are illustrated on a numerical simulation and validated on a benchmark as the continuous stirred tank reactor system.