Frequency identification of nonparametric Wiener systems containing backlash nonlinearities

This paper addresses the problem of identifying Wiener systems constituted of nonparametric linear dynamics and backlash nonlinearities. The linear subsystem is arbitrary but stable. The backlash nonlinearity borders are almost arbitrary-shape. In particular, these are allowed to be nonsmooth, noninvertible and crossing. A frequency identification method is developed to estimate the system frequency response function (at a given set of frequencies) and the backlash nonlinearity borders (within a given working domain). The identification method involves sine excitations and consistent estimators designed using analytic geometry tools, e.g. fictive limit cycles; informative backlash limit cycles; spread- and orientation-compatibility.