On Identification of Discrete Multivariate Hammerstein System by Kernel Regression Estimate

In this paper we discuss estimation of discrete Hammerstein system. The impulse response function of dynamical, linear subsystem is obtained by the correlation method. No conditions whatsoever are imposed on the transform characteristics of nonlinear, memoryless subsystem with multivariate input and single output. The estimation algorithm is given and its local as well as global convergence is shown as the number of measurements tends to infinity. The rates of convergence in both cases are derived under mild conditions on the smoothness of nonlinear system. The performance of the algorithm is tested in the computer simulation.