By Topic

Nonparametric identification of Wiener systems by orthogonal series

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
W. Greblicki ; Inst. of Eng. Cybern., Tech. Univ. Wroclaw, Poland

A Wiener system, i.e., a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade, is identified. Both the input signal and disturbance are random, white, and Gaussian. The unknown nonlinear characteristic is strictly monotonous and differentiable and, therefore, the problem of its recovering from input-output observations of the whole system is nonparametric. It is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed. The estimates apply the trigonometric, Legendre, and Hermite orthogonal functions. Pointwise consistency of all the algorithms is shown. Under some additional smoothness restrictions, the rates of their convergence are examined and compared. An algorithm to identify the impulse response of the linear subsystem is proposed

Published in:

IEEE Transactions on Automatic Control  (Volume:39 ,  Issue: 10 )