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A matrix gradient algorithm for identification of parameterized time‐varying parameters
Author(s) -
Chen MinShin,
Li JyunSian,
Wu PoChing
Publication year - 2009
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.80
Subject(s) - parameterized complexity , matrix (chemical analysis) , convergence (economics) , algorithm , observer (physics) , basis (linear algebra) , mathematics , state transition matrix , series (stratigraphy) , gradient method , computer science , mathematical optimization , control theory (sociology) , symmetric matrix , control (management) , artificial intelligence , paleontology , eigenvalues and eigenvectors , materials science , physics , geometry , quantum mechanics , economics , composite material , biology , economic growth
This paper considers the problem of estimating time‐varying parameters which can be parameterized by a series of arbitrary known basis functions. It is shown that this problem is equivalent to the observer design problem for a “matrix” dynamic system. A “matrix” gradient algorithm, which mimics the well‐known “vector” gradient algorithm, is proposed to estimate the unknown matrix. The contribution of this paper is to show that convergence of the proposed matrix algorithm is guaranteed by the persistent excitations of both the regressor and the basis functions. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society