Contributions to the Statistical Foundation of Data-driven Control

we demonstrate several techniques to prove safety guarantees for robust control problems with statistical structure; that is, for data-driven dynamical modeling or verification problems where uncertainty is modeled by probability. These guarantees are probabilistic in nature, in accordance with the statistical nature of the uncertainty, and can be derived with limited model assumptions. Indeed, some of the techniques require no more than measurability. We focus on two data-driven control problems: estimation of forward reachable sets from data, and robust control of time- and frequency-domain models defined by a Gaussian process regression model. In the former, we apply scenario optimization and statistical learning theory to obtain probabilistic guarantees of accuracy and confidence with minimal system knowledge. In the latter, we apply the theory of suprema of Gaussian processes to establish high-probability regions of attraction, L2 gain bounds, and integral quadratic constraints for the uncertain system