In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning problem. We show a uniform error bound on nonparametric kernel regression under a dynamically-achievable dense sampling scheme. This allows for a finite-time convergence rate on the sub-optimality of using the regressor in closed-loop for waypoint tracking. We demonstrate our results in simulation with simplified unmanned aerial vehicle and autonomous driving examples.
@article{arxiv.2008.12332,
title = {Certainty Equivalent Perception-Based Control},
author = {Sarah Dean and Benjamin Recht},
journal= {arXiv preprint arXiv:2008.12332},
year = {2021}
}