On identification of nonstationary Hammerstein systems by theFourier series regression estimate

摘要

A study is made of the identification of a single-input,single-output (SISO) discrete Hammerstein system. Such a system consistsof a nonlinear, memoryless subsystem followed by a dynamic, linearsubsystem. The authors identify the parameters of the dynamic, linearsubsystem by the correlation method. The main results concern theidentification of the nonlinear, memoryless subsystem. The authorsimpose no conditions on the functional form of the nonlinear subsystem,recovering the nonlinearity using the Fourier series regression estimateand an input process with fixed initial conditions. They prove thedensity-free pointwise convergence of the estimate, that is, that thealgorithm converges for all input densities. The rates of pointwiseconvergence are obtained for smooth input densities and fornonlinearities of the Lipschitz type