NONLINEARITY ESTIMATION IN HAMMERSTEIN SYSTEMS BASED ON ORDERED OBSERVATIONS

The nonlinear subsystem of a Hammerstein system is identified, i.e., i ts characteristic is recovered from input-output observations of the w hole system. The input and disturbance are white stochastic processes, The identified characteristic satisfies a piecewise Lipschitz conditi on only, Algorithms presented in the paper are calculated from ordered input-output observations, i.e., from pairs of observations arranged in a sequence in which input measurements increase in value, The mean integrated square error converges to zero as the number of observation s tends to infinity. Convergence rates are insensitive to the shape of the probability density of the input signal. Results of numerical sim ulation are also shown.