Lecture Series on Statistical Contraction Theory

This lecture series provides useful resources for studying statistical contraction theory for learning-based control of nonlinear dynamical systems, partially addressing the question: “How can we derive mathematically rigorous guarantees for data-driven nonlinear control systems with minimal structural and distributional assumptions?” The following lecture notes are based on materials prepared for the DISC Winter School held at Eindhoven University of Technology in January 2026, organized by Prof. Amritam Das and Prof. Sebastiaan van den Eijnden. You are welcome to use them for any purpose that advances knowledge in this field. When you use a significant portion of them, please cite the relevant papers listed at the beginning of each lecture note.

Our main goal here is to provide a quick overview of the mathematical essentials of this topic, accommodating researchers new to the field and sparking interdisciplinary research. Therefore, this lecture series, including homework assignments, is intended to be completed within 1–2 days with minimal prerequisites. If you are comfortable with Canvas, the same content is available here (https://canvas.illinois.edu/courses/63663) and will be updated regularly. We welcome feedback at hiroyasu@illinois.edu.