Data-Driven LQR Design for LTI systems with Exogenous Inputs

This paper presents a data-driven state feedback control law, based on a linear quadratic regulator (LQR) design, for systems with exogenous inputs. In general, this framework is referred to as a data-driven min-max controller, and is more robust to disturbances than the standard LQR controllers. Instead of relying on system models, in this work, the state feedback control law is computed directly from the knowledge of the inputs and the states. The LQR gain is parametrized with matrices that are directly estimated using open-loop experiment data of the system. We experimentally validate our results by implementing the data driven controller for performance management of a web-server hosted on a private cloud.