A mixed, parametric-non-parametric routine for Hammerstein system identification is presented. Parameters of a non-linear characteristic and of ARMA linear dynamical part of Hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise. Both subsystems are identified separately, thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non-parametric regression function estimation method. A wide class of non-linear characteristics including functions which are not linear in the parameters is admitted. It is shown that the resulting estimates of system parameters are consistent for both white and coloured noise. The problem of generating optimal instruments is discussed and proper non-parametric method of computing the best instrumental variables is proposed. The analytical findings are validated using numerical simulation results.
The paper deals with the problem of reconstruction of nonlinearities in a certain class of nonlinear systems of composite structure from their input-output observations when 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 the Haar multiresolution analysis in particular is applied to construct nonparametric identification techniques of nonlinear characteristics. 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. With applications in mind, the problem 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 computer simulations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.