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Geometric Control Theory

Course Type: 
PhD Course
Academic Year: 
March - May
20 h

"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

Next Lectures: 

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