Robustness and Consistency in Linear Quadratic Control with Predictions
Abstract
We study the problem of learningaugmented 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 $\lambda$confident controller and prove that it maintains a competitive ratio upper bound of $1+\min\{O(\lambda^2\varepsilon)+ O(1\lambda)^2,O(1)+O(\lambda^2)\}$ where $\lambda\in [0,1]$ is a trust parameter set based on the confidence in the predictions, and $\varepsilon$ is the prediction error. Further, we design a selftuning policy that adaptively learns the trust parameter $\lambda$ with a regret that depends on $\varepsilon$ and the variation of perturbations and predictions.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.09659
 Bibcode:
 2021arXiv210609659L
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control
 EPrint:
 31 pages, 4 figures