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IEEE Transactions on Automatic Control
Article . 1988 . Peer-reviewed
License: IEEE Copyright
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Adaptive control of time-varying linear systems

Authors: Middleton, Richard H.; Goodwin, Graham C.;

Adaptive control of time-varying linear systems

Abstract

This well-written paper examines stability and robustness (with respect to unmodeled dynamics) of continuous-time adaptive controllers for linear time-varying continuous-time systems with bounded, slowly varying parameters, or parameters with infrequent jumps. The main stability result is that under all hypotheses stated in the paper (A,B,C,D, etc.) BIBO stability of the system can be achieved under certainty equivalence adaptive control. These results are important as they lend credibility to the use of adaptive control algorithms. The references given are extensive, but some are not easily attained. What is not addressed in this paper are the effects of discretization on the algorithms which is necessary for solution, since the derivatives of the observations are not available. Also, no definitive assessment of the quality of identification or the quality of the adaptation can be determined from the analysis given in this paper. Some points: 1.) The introduction in (2.7)-(2.10) of unmodeled dynamics is somewhat artificially contrived (by adding zero's in (2.7)). 2) The description of unmodeled dynamics in Remark 2.2 ignores the possibility of unmodeled nonlinear dynamics, which is particularly relevant in the case when the model represents a linearization of a nonlinear model. 3) Error bounds such as (3.3) (3.4) or (3.15) (3.16) indicate that the error can grow like the size of the observations. This, in itself, is not very significant.

Related Organizations
Keywords

time-dependent, Adaptive control/observation systems, Linear systems in control theory, Sensitivity (robustness), Input-output approaches in control theory, continuous-time

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
214
Top 1%
Top 1%
Top 10%
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