l2 gain bounded adaptive control of a first order linear system
(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:
https://lup.lub.lu.se/record/536130
- author
- Rantzer, Anders LU
- organization
- publishing date
- 2004
- 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}}, }