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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
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)
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Proceedings of American Control Conference
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American Control Conference 2018
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English
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yes
id
18440cca-ac87-4649-bf81-88667c039c9a
date added to LUP
2018-05-31 09:32:16
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2018-06-13 11:06:46
@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},
  language     = {eng},
  month        = {06},
  title        = {Concentration Bounds for Single Parameter Adaptive Control},
  year         = {2018},
}