Concentration Bounds for Single Parameter Adaptive Control
Rantzer, Anders LU
(2018)
American Control Conference 2018
2018-June.
p.1862-1866
- Abstract
- The purpose of this paper is to analyse transient dynamics in adaptive control using statistical concentration bounds. For maximal clarity, the study is limited to a linear first order system with a single uncertain parameter. Two types of bounds are given: First we prove probabilistic bounds on the parameter estimation error as a function of time. In particular, we prove that the estimation error has finite variance after three time steps and finite fourth moments after five time steps. These bounds are independent of how the parameter estimates are used for feedback. Secondly, we bound the “regret” as a function of time, i.e. the difference in control performance between a self-tuning adaptive controller and the best controller given... (More)
- The purpose of this paper is to analyse transient dynamics in adaptive control using statistical concentration bounds. For maximal clarity, the study is limited to a linear first order system with a single uncertain parameter. Two types of bounds are given: First we prove probabilistic bounds on the parameter estimation error as a function of time. In particular, we prove that the estimation error has finite variance after three time steps and finite fourth moments after five time steps. These bounds are independent of how the parameter estimates are used for feedback. Secondly, we bound the “regret” as a function of time, i.e. the difference in control performance between a self-tuning adaptive controller and the best controller given full knowledge of the plant. The conservatism of the bounds is investigated through simulation. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/18440cca-ac87-4649-bf81-88667c039c9a
- author
- Rantzer, Anders
LU
- organization
- publishing date
- 2018-06-27
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of American Control Conference
- volume
- 2018-June
- article number
- 8431891
- pages
- 1862 - 1866
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- American Control Conference 2018
- conference location
- Milwaukee, Wisconsin, United States
- conference dates
- 2018-06-27 - 2018-06-29
- external identifiers
-
- scopus:85052589887
- ISBN
- 978-153865428-6
- DOI
- 10.23919/ACC.2018.8431891
- language
- English
- LU publication?
- yes
- id
- 18440cca-ac87-4649-bf81-88667c039c9a
- date added to LUP
- 2018-05-31 09:32:16
- date last changed
- 2023-11-17 19:50:23
@inproceedings{18440cca-ac87-4649-bf81-88667c039c9a,
abstract = {{The purpose of this paper is to analyse transient dynamics in adaptive control using statistical concentration bounds. For maximal clarity, the study is limited to a linear first order system with a single uncertain parameter. Two types of bounds are given: First we prove probabilistic bounds on the parameter estimation error as a function of time. In particular, we prove that the estimation error has finite variance after three time steps and finite fourth moments after five time steps. These bounds are independent of how the parameter estimates are used for feedback. Secondly, we bound the “regret” as a function of time, i.e. the difference in control performance between a self-tuning adaptive controller and the best controller given full knowledge of the plant. The conservatism of the bounds is investigated through simulation.}},
author = {{Rantzer, Anders}},
booktitle = {{Proceedings of American Control Conference}},
isbn = {{978-153865428-6}},
language = {{eng}},
month = {{06}},
pages = {{1862--1866}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Concentration Bounds for Single Parameter Adaptive Control}},
url = {{https://lup.lub.lu.se/search/files/44648975/18acc_adaptive.pdf}},
doi = {{10.23919/ACC.2018.8431891}},
volume = {{2018-June}},
year = {{2018}},
}