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l2 gain bounded adaptive control of a first order linear system

Rantzer, Anders LU (2004) In Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
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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Chapter in Book/Report/Conference proceeding
publication status
published
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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
2016-04-16 11:48:39
@misc{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},
  series       = {Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS)},
  title        = {l2 gain bounded adaptive control of a first order linear system},
  year         = {2004},
}