On SelfTuning Regulators
(2001) 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:
https://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
 host publication
 Control Theory: TwentyFive Seminal Papers (19321981)
 editor
 Basar, Tamer
 publisher
 John Wiley and Sons
 external identifiers

 scopus:0034851774
 ISBN
 0780360214
 language
 English
 LU publication?
 yes
 additional info
 Reprint of paper from Automatica vol 9, pages 185199..
 id
 55481ed16f854125aa9c576e52febcff (old id 537831)
 date added to LUP
 20160404 10:55:00
 date last changed
 20210106 08:54:48
@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}, booktitle = {Control Theory: TwentyFive Seminal Papers (19321981)}, editor = {Basar, Tamer}, isbn = {0780360214}, language = {eng}, publisher = {John Wiley and Sons}, title = {On SelfTuning Regulators}, year = {2001}, }