On the identification of additive nonlinear systems

A certain nonlinear system of an adaptive form is identified. Each branch of the system consists of a nonlinear gain followed by a dynamic linear subsystem. Algorithms for recovering characteristics of the system are proposed. The linear subsystem is identified by the correlation technique, whereas the nonlinear part is recovered with the help of orthogonal function techniques for estimation of the regression function. This is carried out by solving a system of integral equations relating to nonlinear characteristics and regression functions. The applied orthogonal functions are related to a diagonal expansion of the input joint probability density function. The conditions for consistency are established and the rate of convergence is evaluated