Identification of Nonlinear Dynamic Systems Using Fuzzy Hammerstein-Wiener Systems

In this paper, a new fuzzy Hammerstein-Wiener model (FHWM) is developed in order to identify a nonlinear dynamic system operating in a stochastic environment. Wherein more general aspect is considered like both non-invertible nonlinearities and stochastic disturbances before the Wiener nonlinearity. The FHWM consists of a linear dynamic subsystem surrounded by two static Takagi-Sugeno (T-S) fuzzy models. The Back Propagation based Gradient method (BPG) is used to determine jointly the parameters and the internal variable of the proposed FHWM. A numerical example is provided to demonstrate the performance of the FHWM.