Low-complexity learning of Linear Quadratic Regulators from noisy data

This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller without estimating a model of the system. Sufficient conditions are given under which this method returns a stabilizing controller with guaranteed relative error when the data used to design the controller are affected by noise. This method has low complexity as it only requires a finite number of samples of the system response to a sufficiently exciting input, and can be efficiently implemented as a semi-definite programme. (C) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper proposes a method to return a controller without estimating a model of the system, and provides sufficient conditions for returning a stabilizing controller when the data is affected by noise. The method has low complexity, requiring only a finite number of samples and can be efficiently implemented.