Identification of discrete Hammerstein systems by the Fourier series regression estimate

Abstract

The identification of a single-input, single-output (SISO) discrete Hammerstein system is studied. Such a system consists of a non-linear memoryless subsystem followed by a dynamic, linear subsystem. The parameters of the dynamic, linear subsystem are identified by a correlation method and the Newton-Gauss method. The main results concern the identification of the non-linear, memoryless subsystem. No conditions are imposed on the functional form of the non-linear subsystem, recovering the non-linear using the Fourier series regression estimate. The density-free pointwise convergence Of the estimate is proved, that is.algorithm converges for all input densities The rate of pointwise convergence is obtained for smooth input densities and for non-linearities of Lipschitz type.Globle convergence and its rate are also studied for a large class of non-linearities and input densities