On Nonparametric Identification of Multi-Channel Hammerstein Systems

The paper deals with the problem of identification of a class of nonlinear dynamical systems of the multi-channel form. The examined system is the multi-channel generalization of the classical Hammerstein model. The a priori information about the system nonlinearities is very limited excluding any parametric approach to the problem. The modern statistical theory of nonparametric regression along with the marginal integration approach are applied to form estimates of the nonlinearities. In particular the generalized kernel regression techniques are used to construct the identification algorithms. Pointwise convergence rates of the proposed estimates are evaluated. A striking feature of one of our identification algorithm is its ability to decouple the estimation problem related to each channel. This is a surprising result since the input signals are dependent with completely unknown joint probability density function.