Data-Driven Distributionally Robust LQR with Multiplicative Noise
Abstract
We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.
Cite
Text
Coppens et al. "Data-Driven Distributionally Robust LQR with Multiplicative Noise." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.Markdown
[Coppens et al. "Data-Driven Distributionally Robust LQR with Multiplicative Noise." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.](https://mlanthology.org/l4dc/2020/coppens2020l4dc-datadriven/)BibTeX
@inproceedings{coppens2020l4dc-datadriven,
title = {{Data-Driven Distributionally Robust LQR with Multiplicative Noise}},
author = {Coppens, Peter and Schuurmans, Mathijs and Patrinos, Panagiotis},
booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control},
year = {2020},
pages = {521-530},
volume = {120},
url = {https://mlanthology.org/l4dc/2020/coppens2020l4dc-datadriven/}
}