Recursive identification for Hammerstein systems with hybrid static nonlinearities and asymmetric ARX

In this paper, an iterative identification for the Hammerstein model, which consists of a static nonlinear part in cascade with a linear dynamic part, is introduced. Therein, the static nonlinear part is composed of two-segment polynomials in series with dead-zone nonlinearities, while the linear part takes on the asymmetric ARX (autoregressive with exogenous inputs) dynamics. For the Hammerstein system, the so-called key-term separation principle was firstly implemented to separate the parameters of both the static nonlinear sub-model and dynamic block. Thereafter, the system output is represented by a special form of linear combination of the parameters. Then, a modified Recursive General Least Squares Algorithm (RGLS) was introduced for the iterative estimation of the parameters. Finally, the presented simulation results had validated the effectiveness of the proposed method.