Title :
Revisiting the Two-Stage Algorithm for Hammerstein system identification
Author :
Wang, Jiandong ; Zhang, Qinghua ; Ljung, Lennart
Author_Institution :
Dept. of Ind. Eng. & Manage., Peking Univ., Beijing, China
Abstract :
The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of block-oriented nonlinear systems including Hammerstein systems. This paper revisits an optimality result established by Bai in 1998 showing that the TSA provides the optimal estimation of a bilinearly parameterized Hammerstein system in the sense of a weighted nonlinear least-squares (LS) criterion formulated with some special weighting matrix. We will re-derive this result through the Lagrange multiplier method which is more constructive, and complement it by giving a complete parametrization of the special weighting matrices. Numerical examples of Hammerstein system identification are presented to validate the obtained theoretical results.
Keywords :
bilinear systems; identification; least squares approximations; matrix algebra; nonlinear control systems; Hammerstein system identification; Lagrange multiplier method; bilinearly parameterized system; block oriented nonlinear systems; optimal estimation; two-stage algorithm; weighted nonlinear least squares criterion; weighting matrix; Actuators; Lagrangian functions; Least squares approximation; Linear regression; Nonlinear distortion; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Parameter estimation; System identification;
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5400243
