Improved Solution of Equations by Regularizing Ill-Conditioned Coefficient Matrix for System Identification

A numerical method is proposed for solving a set of simultaneous equations with an ill-conditioned coefficient matrix to apply system identification. To find an approximate solution, the coefficient matrix is regularized by adding a small positive value ε to its diagonal terms. A regularized matrix...

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Bibliographic Details
Published in:AIAA journal 2013-09, Vol.51 (9), p.2076-2085
Main Authors: Misawa, Masayoshi, Sekiya, Takashi, Oba, Masaki
Format: Article
Language:English
Subjects:
Aerodynamics
Applied sciences
Approximation
Coefficients
Computer science
control theory
systems
Control theory. Systems
Estimates
Exact sciences and technology
Mathematical analysis
Mathematical models
Modelling and identification
Numerical analysis
Numerical methods
Simultaneous equations
System identification
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Summary:A numerical method is proposed for solving a set of simultaneous equations with an ill-conditioned coefficient matrix to apply system identification. To find an approximate solution, the coefficient matrix is regularized by adding a small positive value ε to its diagonal terms. A regularized matrix is provided in different expressions that depend on the coefficient matrix. This paper regularizes a rectangular coefficient matrix and then a square coefficient matrix. Improvement of solution accuracy is possible by removing the very small singular values. Therefore, rank estimation of the coefficient matrix is a key to obtaining an accurate solution. This paper gives a method that estimates the rank by setting an appropriate value of ε. Numerical examples show that the proposed method is effective for system identification.
ISSN:0001-1452
1533-385X
DOI:10.2514/1.J051394