On identification of non-linear two-channel Hammerstein systems

This paper deals with the problem of reconstruction of nonlinearities in a certain class of nonlinear dynamical systems of the multi-channel form. Each channel of the system has a nonlinearity in series connection with a linear time-invariant system. Such a model is often referred to as the Hammerstein system. 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, kernel regression techniques are used to construct the identification algorithms. The proposed estimates are able 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. Pointwise convergence properties of the proposed estimation procedures are established and convergence rates are evaluated. Computer simulations are included to verify the theory.