Non-parametric system identification of non-linear block-oriented systems by multiscale expansions

The paper deals with the problem of reconstruction of nonlinearities in a certain class of nonlinear dynamical systems of composite structure from their input-output observations when a prior information about the system is poor, thus excluding the standard parametric approach to the problem. The multiresolution idea, being the fundamental concept of modern wavelet theory, is adopted and multiscale expansions associated with scaling and wavelet functions of compact support are applied to construct non-parametric identification techniques of nonlinear characteristics. Conditions for the convergence are given and for nonlinearities satisfying some smoothing conditions the rate of convergence is evaluated.