NONLINEAR-SYSTEM IDENTIFICATION BY THE HAAR MULTIRESOLUTION ANALYSIS

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.