On Identification of Discrete Hammerstein Systems by the Fourier Series Regression Estimate

Abstract

We study the identification of single-input, single-output discrete Hammerstein system. We identify the parameters of the dynamic, linear subsystem by the correlation and Newton-Gauss method. The main results concern the identification of the nonlinear, memoryless subsystem. We impose no conditions on the functional form of the nonlinear subsystem, recovering the nonlinearity using the Fourier series regression estimate. We prove the density-free pointwise convergence of the estimate. The rates of pointwise convergence are obtained for smooth input densities and for nonlinearities of Lipschitz type.