M. Pawlak et Z. Hasiewicz, NONLINEAR-SYSTEM IDENTIFICATION BY THE HAAR MULTIRESOLUTION ANALYSIS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 45(9), 1998, pp. 945-961
The paper deals with the problem of reconstruction of nonlinearities i
n a certain class of nonlinear systems of composite structure from the
ir input-output observations when prior information about the system i
s poor, thus excluding the standard parametric approach to the problem
. The multiresolution idea, being the fundamental concept of modern wa
velet theory, is adopted, and the Haar multiresolution analysis in par
ticular is applied to construct nonparametric identification technique
s of nonlinear characteristics. The pointwise convergence properties o
f the proposed identification algorithms are established. Conditions f
or the convergence are given; and for nonlinearities satisfying a loca
l Lipschitz condition, the rate of convergence is evaluated. With appl
ications in mind, the problem of data-driven selection of the optimum
resolution degree in the identification procedure, essential for the m
ultiresolution analysis, is considered as well, The theory is verified
in the computer simulations.