The mini-course of 6 lectures will be devoted to introduction to geometric control theory and its applications. It will cover the questions of controllability, optimal control, and sub-Riemannian geometry. Applications will include PDEs, metric geometry on Lie groups, mechanics, robotics, and vision.
The lecture course include the following topics:
1. Examples and statements of control problems
2. Local controllability of nonlinear systems
3. Orbit theorem, Frobenius theorem, Krener’s theorem
4. Pontryagin maximum principle
5. Sub-Riemannian geometry on Lie groups
6. Applications of sub-Riemannian geometry to PDEs and metric geometry on Lie groups
7. Applications of geometric control to mechanics, robotics, and vision.
3.15-4.1.pdf
