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l2 gain bounded adaptive control of a first order linear system

Rantzer, Anders LU orcid (2004)
Abstract
The problem of adaptive control is considered from a perspective of l2-gain. It has recently been shown that without an a priori bound on the system parameters, there exists no single dynamic feedback law that achieves bounded gain from disturbances to state for all first order linear systems. In this paper, a converse statement is proved for a standard adaptive scheme where the parameter estimate is saturated at a prespecified level. It is proved that the l2-gain with this controller grows at most linearly with the size of the a priori bound on the unknown parameter.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
ISBN
90-5682-517-8
language
English
LU publication?
yes
id
7568f94b-3cfc-4ad1-a457-b5a11f872432 (old id 536130)
date added to LUP
2016-04-04 13:53:24
date last changed
2018-11-21 21:17:00
@inproceedings{7568f94b-3cfc-4ad1-a457-b5a11f872432,
  abstract     = {{The problem of adaptive control is considered from a perspective of l2-gain. It has recently been shown that without an a priori bound on the system parameters, there exists no single dynamic feedback law that achieves bounded gain from disturbances to state for all first order linear systems. In this paper, a converse statement is proved for a standard adaptive scheme where the parameter estimate is saturated at a prespecified level. It is proved that the l2-gain with this controller grows at most linearly with the size of the a priori bound on the unknown parameter.}},
  author       = {{Rantzer, Anders}},
  booktitle    = {{Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)}},
  isbn         = {{90-5682-517-8}},
  language     = {{eng}},
  title        = {{l2 gain bounded adaptive control of a first order linear system}},
  year         = {{2004}},
}