"Geometric Control Theory” by Ugo Boscain (CNRS, LJLL, Sorbonne Université, and INRIA), Paris)

Lecture 1: Introduction to control theory: controllability, stability, optimal control.

Lecture 2: Families of vector fields. Lie brackets, The Frobenius theorem, the Chow theorem, the Krener theorem.

Lecture 3: The theory of compatible vector fields. Recurrent drift. Applications to quantum mechanical systems.

Lecture 4: Optimal Control. Existence. The Pontryagin Maximum Principle (part 1).

Lecture 5: The Pontryagin Maximum Principle (part 2). Abnormal extremals and singular trajectories.

Lecture 6: Riemannian geometry and generalizations (sub-Riemannian geometry, Almost-Riemannian geometry).

Lecture 7: The Heisenberg group, The Grushin plane. The Martinet distribution.

Lecture 8: Minimum time for affine systems. Applications

Lecture 9: The Fuller phenomenon.

Remark: Lectures 6 and 7 will be coordinated with the course of sub-Riemannian geometry of Luca Rizzi