An optimal two-stage identification algorithm for Hammerstein–Wiener nonlinear systems

Abstract

An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.