Non-parametric identification of multi-channel systems by multiscale expansions

The paper deals with the problem of reconstruction of nonlinearities in a certain class of nonlinear dynamical systems of the multichannel form. A prior information about the system is very limited excluding the standard parametric approach to the problem. The system structure consists of nonlinearities being embedded in a block oriented structure containing dynamic linear subsystems and other “nuisance” nonlinearities. The multiresolution idea, being the fundamental concept of the modern wavelet theory, is adopted and multiscale expansions associated with a large class of scaling functions are applied to construct nonparametric identification techniques of the nonlinearities. The pointwise convergence properties of the proposed identification algorithms are established. Conditions for the convergence are given; and for nonlinearities satisfying a local Lipschitz condition, the rate of convergence is evaluated.