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Type: Journal article
Title: Best causal mathematical models for a nonlinear system
Author: Torokhti, A.
Howlett, P.
Pearce, C.
Citation: IEEE Transactions on Circuits and Systems Part 1: Regular Papers, 2005; 52(5):1013-1020
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2005
ISSN: 1057-7122
Statement of
Anatoli Torokhti, Phil Howlett, and Charles Pearce
Abstract: We provide new causal mathematical models of a nonlinear system S which are specifications of a nonlinear operator P/sub p/ of degree p=1,2,.... The operator P/sub p/ is determined from a special orthogonalization procedure and minimization of the mean squared difference between outputs of S and P/sub p/. As a result, these models have smallest possible associated errors in the class of such operators P/sub p/. The causality condition is implemented through the use of specific matrices called lower trapezoidal. The associated computational work is reduced by the use of the orthogonalization procedure. We provide a strict justification of the proposed approach including theorems on an explicit representatoin of the models' parameters, and theorems on the associated error representation. The possible extensions of the proposed approach and its potential applications are outlined.
Keywords: Causality
input–output map
nonlinear systems
Description: ©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
DOI: 10.1109/TCSI.2005.846673
Appears in Collections:Applied Mathematics publications
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