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Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm
Author(s) -
Bejarano F.J.,
Fridman L.,
Poznyak A.
Publication year - 2007
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.1190
Subject(s) - observability , bounded function , state vector , observer (physics) , mathematics , rank condition , estimator , state (computer science) , control theory (sociology) , rank (graph theory) , hierarchy , algorithm , identifiability , scalar (mathematics) , computer science , control (management) , artificial intelligence , mathematical analysis , statistics , physics , geometry , classical mechanics , quantum mechanics , combinatorics , controllability , economics , market economy
A robust hierarchical observer is designed for linear time invariant systems with unknown bounded inputs under conditions of strong observability, providing exact state estimation. The main condition for designing the state estimator is the, so‐called, strong observability condition. The supertwisting (second‐order sliding mode) algorithm is used in each step of the hierarchy; the continuity of the supertwisting output injection allows to reconstruct a vector formed by some full column rank matrix premultiplied by the state vector, and that vector is obtained in a finite time and without any sort of filtration . For the case when the unknown inputs are considered as constant uncertain parameters, the continuous version of the least‐square method is developed. Two numerical examples illustrate the efficiency of the suggested technique. Copyright © 2007 John Wiley & Sons, Ltd.