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On Self-Tuning Regulators

Åström, Karl Johan LU and Wittenmark, Björn LU (1973) In Automatica 9(2). p.185-199
Abstract
The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analysed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and certain cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear... (More)
The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analysed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and certain cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear stochastic nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Automatica
volume
9
issue
2
pages
185 - 199
publisher
Pergamon
external identifiers
  • Scopus:0001642818
ISSN
0005-1098
DOI
10.1016/0005-1098(73)90073-3
language
English
LU publication?
yes
id
e907c5c5-99db-46a9-b86d-bcfb33754108 (old id 4857035)
date added to LUP
2014-12-04 11:58:32
date last changed
2016-11-13 04:35:52
@misc{e907c5c5-99db-46a9-b86d-bcfb33754108,
  abstract     = {The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analysed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and certain cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear stochastic nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer.},
  author       = {Åström, Karl Johan and Wittenmark, Björn},
  issn         = {0005-1098},
  language     = {eng},
  number       = {2},
  pages        = {185--199},
  publisher    = {ARRAY(0x7e32908)},
  series       = {Automatica},
  title        = {On Self-Tuning Regulators},
  url          = {http://dx.doi.org/10.1016/0005-1098(73)90073-3},
  volume       = {9},
  year         = {1973},
}