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Robustness and Consistency in Linear Quadratic Control with Predictions

Li, Tongxin and Yang, Ruixiao and Qu, Guannan and Shi, Guanya and Yu, Chenkai and Wierman, Adam and Low, Steven (2021) Robustness and Consistency in Linear Quadratic Control with Predictions. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210716-225846876

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Abstract

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances consistency, which measures the competitive ratio when predictions are accurate, and robustness, which bounds the competitive ratio when predictions are inaccurate. We propose a novel λ-confident controller and prove that it maintains a competitive ratio upper bound of 1 + min {O(λ²ε) + O(1−λ)², O(1)+O(λ²)} where λ ∈ [0,1] is a trust parameter set based on the confidence in the predictions, and ε is the prediction error. Further, we design a self-tuning policy that adaptively learns the trust parameter λ with a regret that depends on ε and the variation of perturbations and predictions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2106.09659arXivDiscussion Paper
ORCID:
AuthorORCID
Li, Tongxin0000-0002-9806-8964
Qu, Guannan0000-0002-5466-3550
Shi, Guanya0000-0002-9075-3705
Low, Steven0000-0001-6476-3048
Additional Information:Attribution 4.0 International (CC BY 4.0).
Record Number:CaltechAUTHORS:20210716-225846876
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210716-225846876
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109906
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:16 Jul 2021 23:23
Last Modified:16 Jul 2021 23:23

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