Data-driven optimal control of linear time-invariant systems

Abstract

We consider an optimal control problem for discrete-time linear time-invariant systems subject to unknown state-space model, constrained inputs and noisy output measurements. Since traditional model-based optimal control problem formulations and methods are not applicable to the problem under consideration, we propose a data-driven robust formulation based on the explicit model description derived from a single measured trajectory of the system. Then we propose an open-loop optimal feedback control scheme and show that its efficient implementation requires solution of a number of optimal estimation problems and a deterministic optimal control problem, all in data-driven formulations. The main contributions of this paper are the separation of the estimation and control processes in the data-driven context and the resulting robust feedback control scheme.