On SelfTuning Regulators
(1973) In Automatica 9(2). p.185199 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 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 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... (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 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 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 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4857035
 author
 Åström, Karl Johan ^{LU} and Wittenmark, Björn ^{LU}
 organization
 publishing date
 1973
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Automatica
 volume
 9
 issue
 2
 pages
 185  199
 publisher
 Pergamon
 external identifiers

 scopus:0001642818
 ISSN
 00051098
 DOI
 10.1016/00051098(73)900733
 language
 English
 LU publication?
 yes
 id
 e907c5c599db46a9b86dbcfb33754108 (old id 4857035)
 date added to LUP
 20141204 11:58:32
 date last changed
 20180805 04:27:33
@article{e907c5c599db46a9b86dbcfb33754108, 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 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 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 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 = {00051098}, language = {eng}, number = {2}, pages = {185199}, publisher = {Pergamon}, series = {Automatica}, title = {On SelfTuning Regulators}, url = {http://dx.doi.org/10.1016/00051098(73)900733}, volume = {9}, year = {1973}, }