Best approximation of operators in the modeling of nonlinear systems

We propose and justify a new method for the best constructive approximation of input-output maps of nonlinear systems transforming stochastic signals. The approximant is produced by a polynomial operator and minimizes the mean-square error between a desired output signal and the output signal of the approximating system. The error equation associated with this procedure is established. Numerical simulations demonstrate the efficiency of the proposed approach. The new method provides a significantly better performance than the technique considered by the authors previously (2001).