Data-driven Distributionally Robust LQR with Multiplicative Noise

Authors

Peter Coppens, Mathijs Schuurmans, Panagiotis Patrinos

Year

2019

Journal Paper

Source

Learning for Dynamics and Control

Identifiers

arXiv 1912.09990

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.