Rimantas Pupeikis, Parametric Identification of Linear Systems Followed by Non-Invertible Piecewise Nonlinearities, IFSL Volume 6, International Frontier Science Letters (Volume 6)
https://www.scipress.com/IFSL.6.16
Abstract:
    The aim of the given paper is the development of an approach for parametric identification of <i>Wiener</i> systems with static non-invertible function, i.e., when the linear part with unknown parameters is followed by piecewise linear nonlinearity with negative slopes. It is shown here that the problem of identification of a nonlinear <i>Wiener</i> system could be reduced to a linear parametric estimation problem by a simple input-output data reordering and by a following data partition into three data sets. A technique based on ordinary least squares (<i>LS</i>) is proposed here for the separate estimation of parameters of linear and nonlinear parts of the <i>Wiener</i> system, including the unknown threshold of piecewise nonlinearity, by processing respective particles of input-output observations. The simulation results are given.
Keywords:
    Missing Observations, Non-Invertible Nonlinearity, Nonlinear Systems, Parametric Identification, <i>Wiener</i> System