The paper deals with the problem of reconstruction of nonlinearities in a certain class of nonlinearsystems of composite structure from their input-output observations when prior information about thesystem is poor, thus excluding the standard parametric approach to the problem. The multiresolutionidea, being the fundamental concept of modern wavelet theory, is adopted, and the Haarmultiresolution analysis in particular is applied to construct nonparametric identification techniques ofnonlinear characteristics. The pointwise convergence properties of the proposed identificationalgorithms are established. Conditions for the convergence are given; and for nonlinearities satisfyinga local Lipschitz condition, the rate of convergence is evaluated. With applications in mind, theproblem of data-driven selection of the optimum resolution degree in the identification procedure,essential for the multiresolution analysis, is considered as well. The theory is verified in the computersimulations.
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