All Data-Driven LQR Algorithms Require at Least as Much Interval Data as System Identification

Abstract

We show that algorithms for solving continuous-time infinite-horizon LQR problems using input and state data on intervals require at least as much data as system identification. Using this result, we show that the map from interval data to the optimal gain defined by these algorithms is continuous. We then obtain a convergence criterion that allows us to approximate the optimal gain by using sampled data in place of interval data. In doing so, we uncover a connection with the theory of numerical integration. We corroborate our theoretical results with some numerical experiments, which show how judicious selection of sample points can significantly improve the accuracy of the approximation.