Identification of Nonlinear Systems using Orthonormal Bases

In this paper, non iterative algorithms for the identification of (multivariable) nonlinear systems consisting of the interconnection of LTI systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Three different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, the Wiener model, and the Feedback Block-Oriented model. For the Hammerstein model, the algorithm provides consistent estimates even in the presence of coloured output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model and the Feedback Block-Oriented model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the systems. An additional advantage of this is the possibility of incorporating prior information about the system in a typically black-box identification scheme.