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l2 gain bounded adaptive control of a first order linear system

Rantzer, Anders LU (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.
Please use this url to cite or link to this publication:
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
2007-09-24 16:43:55
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},
  isbn         = {90-5682-517-8},
  language     = {eng},
  title        = {l2 gain bounded adaptive control of a first order linear system},
  year         = {2004},
}