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
@article{arxiv.1912.09990,
title = {Data-driven distributionally robust LQR with multiplicative noise},
author = {Peter Coppens and Mathijs Schuurmans and Panagiotis Patrinos},
journal= {arXiv preprint arXiv:1912.09990},
year = {2020}
}
Comments
Extended technical report. Accepted for oral presentation at L4DC2020