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Concentration Bounds for Single Parameter Adaptive Control

Rantzer, Anders LU (2018) American Control Conference 2018 In Proceedings of American Control Conference 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:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Proceedings of American Control Conference
volume
2018-June
pages
1862 - 1866
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
American Control Conference 2018
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
2018-10-17 13:23:25
@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    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {Concentration Bounds for Single Parameter Adaptive Control},
  url          = {http://dx.doi.org/10.23919/ACC.2018.8431891},
  volume       = {2018-June},
  year         = {2018},
}