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Identification of linear parameter varying models
Author(s) -
Bamieh Bassam,
Giarré Laura
Publication year - 2002
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.706
Subject(s) - nonlinear system , estimation theory , mathematics , scheduling (production processes) , polynomial , identification (biology) , polynomial regression , mathematical optimization , computer science , control theory (sociology) , linear regression , algorithm , statistics , mathematical analysis , artificial intelligence , botany , control (management) , quantum mechanics , biology , physics
We consider identification of a certain class of discrete‐time nonlinear systems known as linear parameter varying system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dependence of the system coefficients on the parameters is known. We show how this identification problem can be reduced to a linear regression, and provide compact formulae for the corresponding least mean square and recursive least‐squares algorithms. We derive conditions on persistency of excitation in terms of the inputs and scheduling parameter trajectories when the functional dependence is of polynomial type. These conditions have a natural polynomial interpolation interpretation, and do not require the scheduling parameter trajectories to vary slowly. This method is illustrated with a simulation example using two different parameter trajectories. Copyright © 2002 John Wiley & Sons, Ltd.