On SelfTuning Regulators
(2001) In Control Theory: TwentyFive Seminal Papers (19321981) Abstract
 The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time singleinput singleoutput systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. 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 crosscovariances 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 nth order... (More)
 The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time singleinput singleoutput systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. 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 crosscovariances 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 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.
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Reprint of paper from Automatica vol 9, pages 185199 available at http:dx.doi.org/10.1016/00051098(73)900733 (restricted access) (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/537831
 author
 Åström, Karl Johan ^{LU} and Wittenmark, Björn ^{LU}
 organization
 publishing date
 2001
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 in
 Control Theory: TwentyFive Seminal Papers (19321981)
 editor
 Basar, Tamer and
 publisher
 John Wiley & Sons
 external identifiers

 scopus:0034851774
 ISBN
 0780360214
 language
 English
 LU publication?
 yes
 id
 55481ed16f854125aa9c576e52febcff (old id 537831)
 date added to LUP
 20070912 20:13:50
 date last changed
 20180107 10:37:04
@inbook{55481ed16f854125aa9c576e52febcff, abstract = {The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time singleinput singleoutput systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. 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 crosscovariances 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 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.<br/><br> .<br/><br> <br/><br> Reprint of paper from Automatica vol 9, pages 185199 available at http:dx.doi.org/10.1016/00051098(73)900733 (restricted access)}, author = {Åström, Karl Johan and Wittenmark, Björn}, editor = {Basar, Tamer}, isbn = {0780360214}, language = {eng}, publisher = {John Wiley & Sons}, series = {Control Theory: TwentyFive Seminal Papers (19321981)}, title = {On SelfTuning Regulators}, year = {2001}, }