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Identification of Multivariable Linear Systems of Unknown Structure by the Prior Knowledge Fitting Method

Valis, Jaroslav (1970) In Research Reports TFRT-3023
Abstract
This report deals with identification of multivariable linear systems of finite order from measurements of input-output signals when the outputs are corrupted by additive random noises. The input-output relations of such systems can be described by a vector difference equation. A canonical form for the matrix coefficients of this equation is proposed and its existence and uniqueness are shown. This canonical form enables the identification of the structure of matrix coefficients by straightforward search, which drastically reduces the number of different structures, whose "fit" is otherwise to be tested. <br><br> An application of the prior knowledge fitting method for identification of the structure of the matrix coefficients... (More)
This report deals with identification of multivariable linear systems of finite order from measurements of input-output signals when the outputs are corrupted by additive random noises. The input-output relations of such systems can be described by a vector difference equation. A canonical form for the matrix coefficients of this equation is proposed and its existence and uniqueness are shown. This canonical form enables the identification of the structure of matrix coefficients by straightforward search, which drastically reduces the number of different structures, whose "fit" is otherwise to be tested. <br><br> An application of the prior knowledge fitting method for identification of the structure of the matrix coefficients and estimation of their elements, based on the (assumed) independence of noises and input signals, is described. No knowledge of statistical characteristics of the noises is needed, only their mean values are assumed to be constant in time. This method is finite (i.e. no iterations are used, no troubles with convergence etc.). <br><br> The required place in the computer memory does not grow with increasing length of observation of input-output data, as they need not to be stored; all information from the whole past history needed for identification of all examined structures is preserved in a relatively small matrix. <br><br> With increasing length of input-output data the obtained estimates converge to their true values with probability one. <br><br> A FORTRAN IV subroutine for this method, called MIMOID, was written and tested. The results confirm its usefulness. (Less)
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Book/Report
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published
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in
Research Reports TFRT-3023
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
ISSN
0346-5500
language
English
LU publication?
no
id
e7abdf7b-2ef6-40c2-845c-1bf8cba5f77b (old id 8601133)
date added to LUP
2016-04-01 16:23:50
date last changed
2025-04-04 14:01:46
@techreport{e7abdf7b-2ef6-40c2-845c-1bf8cba5f77b,
  abstract     = {{This report deals with identification of multivariable linear systems of finite order from measurements of input-output signals when the outputs are corrupted by additive random noises. The input-output relations of such systems can be described by a vector difference equation. A canonical form for the matrix coefficients of this equation is proposed and its existence and uniqueness are shown. This canonical form enables the identification of the structure of matrix coefficients by straightforward search, which drastically reduces the number of different structures, whose "fit" is otherwise to be tested. &lt;br&gt;&lt;br&gt; An application of the prior knowledge fitting method for identification of the structure of the matrix coefficients and estimation of their elements, based on the (assumed) independence of noises and input signals, is described. No knowledge of statistical characteristics of the noises is needed, only their mean values are assumed to be constant in time. This method is finite (i.e. no iterations are used, no troubles with convergence etc.). &lt;br&gt;&lt;br&gt; The required place in the computer memory does not grow with increasing length of observation of input-output data, as they need not to be stored; all information from the whole past history needed for identification of all examined structures is preserved in a relatively small matrix. &lt;br&gt;&lt;br&gt; With increasing length of input-output data the obtained estimates converge to their true values with probability one. &lt;br&gt;&lt;br&gt; A FORTRAN IV subroutine for this method, called MIMOID, was written and tested. The results confirm its usefulness.}},
  author       = {{Valis, Jaroslav}},
  institution  = {{Department of Automatic Control, Lund Institute of Technology (LTH)}},
  issn         = {{0346-5500}},
  language     = {{eng}},
  series       = {{Research Reports TFRT-3023}},
  title        = {{Identification of Multivariable Linear Systems of Unknown Structure by the Prior Knowledge Fitting Method}},
  url          = {{https://lup.lub.lu.se/search/files/4660706/8625800.pdf}},
  year         = {{1970}},
}