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Variable structure robust state and parameter estimator
Author(s) -
Poznyak Alex S.,
Martínez Joel Correa
Publication year - 2001
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.650
Subject(s) - observability , control theory (sociology) , mathematics , estimator , upper and lower bounds , state variable , observer (physics) , variable (mathematics) , duffing equation , inverted pendulum , transformation (genetics) , nonlinear system , computer science , mathematical analysis , control (management) , biochemistry , statistics , physics , chemistry , quantum mechanics , artificial intelligence , gene , thermodynamics
The problem of simultaneous robust state and parameters estimation for a class of SISO non‐linear systems under mixed uncertainties (unmodelled dynamics as well as observation noises) is addressed. A non‐linear variable structure robust ‘observer–identifier’ is introduced to obtain the corresponding estimates. Lie derivative technique is used to obtain the observability conditions for the equivalent extended non‐linear system. It is shown that, in general, the extended system can lose the global observability property and a special procedure is needed to work well in this situation. The suggested adaptive observer has the non‐linear high‐gain observer structure with adjusted parameters that provides ‘a good’ upper bound for the identification error performance index. The van der Monde transformation is used to derive this bound which turns out to be tight. Three examples dealing with a simple pendulum, the Duffing equation and the van del Pol oscillator are considered to illustrate the effectiveness of the suggested approach. Copyright © 2001 John Wiley & Sons, Ltd.