Data-driven control handling noisy input-state data and noisy input-output data: a survey of trends and techniques

Designing controllers directly from measurement data has attracted growing attention in recent years, as it avoids the need for accurate system modeling or explicit system identification. This paper focuses on recent advances in data-driven control for linear discrete-time systems with unknown system matrices. For noisy input-state data, an in-depth analysis is provided on several representative approaches, including data-driven control based on Willems et al.'s fundamental lemma, quadratic matrix inequalities, linear fractional transformations for combining prior knowledge with data, and integral quadratic constraints. For noisy input-output data, a concise review is presented on control methods based on quadratic matrix inequalities, along with key insights into their structure and implications. The paper concludes by outlining several challenging problems that merit further investigation in future research.