Revisiting the Two-Stage Algorithm for Hammerstein system identification

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.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000336893604019&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Automation & Control SystemsEngineering, Electrical & ElectronicEICPCI-S(ISTP)