A Tutorial on the Non-Asymptotic Theory of System Identification

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of-mainly linear-system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as the covering technique, the Hanson-Wright Inequality and the method of self-normalized martingales. We then employ these tools to give streamlined proofs of the performance of various least-squares based estimators for identifying the parameters in autoregressive models. We conclude by sketching out how the ideas presented herein can be extended to certain nonlinear identification problems. Note: For reasons of space, proofs have been omitted in this version and are available in an online version: https://arxiv.org/abs/2309.03873.