Parameter learning of multi-input multi-output Hammerstein system with measurement noises utilizing combined signals

In this article, the parameter learning scheme for the multi-input multi-output (MIMO) Hammerstein nonlinear systems under measurement noises is studied, which is derived by exploiting the correlation analysis and data filtering technique. The coupled MIMO Hammerstein system presented involves a static nonlinear subsystem modeled by neural fuzzy model (NFM), and a dynamic linear subsystem established by autoregressive moving average with extra input (ARMAX) model. To learn the unknown parameter of the MIMO Hammerstein system, the combined signals are designed to realize that identification of the nonlinear subsystem is separated from that of linear subsystem. First, the correlation properties of separable signals in a nonlinear system are analyzed, then the parameters of the linear subsystem are estimated utilizing correlation analysis, which can deal with the issue of unmeasured intermediate variable in the Hammerstein system. Second, the data filtering technique is introduced to derive the data filtering-based recursive least squares technique for learning the nonlinear subsystem parameter, which can reduce the impact of the moving average noise and improve the precision of parameter estimation. Finally, the effectiveness and feasibility of the proposed identification scheme is proved by numerical simulation and nonlinear pH process.