One-shot set-membership identification of Generalized Hammerstein–Wiener systems

In this paper we consider the identification of Generalized Hammerstein–Wiener systems in the presence of bounded noise affecting both the input and the output sequences. The considered class of systems is characterized by the cascade connection of Hammerstein building blocks, where the nonlinear static input map is a polynomial, which is not assumed to be invertible. The problem of computing the parameter uncertainty intervals is formulated in terms of a set of suitable semialgebraic optimization problems, where both the parameter to be estimated and the inner unmeasurable signals connecting all the subsystems are considered as decision variables. The effectiveness of the proposed algorithm is shown by means of a numerical simulation example. The presented approach is also applied to the problem of identifying the mathematical model of a JFET amplifier from a set of experimentally collected data.