Data-driven continuous-time optimal control: a unified framework using orthogonal functions

Abstract We study data-driven optimal control of continuous-time linear systems over finite- and infinite-time horizons. Our approach builds on our continuous-time version of Willems et al.’s fundamental lemma and on the use of orthogonal basis functions to approximate system trajectories. We show that the solution to an optimal control problem can be approximated by a finite linear combination of basis functions and we establish error bounds for such approximations. Moreover, we approximately solve the algebraic Riccati equation and the associated optimal controller gain directly from data, opening up the possibility of optimal controller design directly from data analogue devices.