As the systems we control become more complex, first-principle modeling becomes either impossible or intractable, motivating the use of machine learning techniques for the control of systems with continuous action spaces. As impressive as the empirical success of these methods have been, strong theoretical guarantees of performance, safety, or robustness are few and far between. This manuscript takes a step towards such providing such guarantees by establishing finite-data performance guarantees for identifying and controlling fully- or partially-unknown dynamical systems.

In this manuscript, we explore three different viewpoints that each provide different quantitative guarantees of performance. First, we present a generalization of the classical theory of integral quadratic constraints. This generalization leads to a tractable computational procedure for finding exponential stability certificates for partially-unknown feedback systems. Second, we present non-asymptotic lower and upper bounds for core problems in the field of system identification. Finally, using the recently developed system-level synthesis framework and tools from high-dimensional statistics, we establish finite-sample performance guarantees for robust output-feedback control of an unknown dynamical system.