- Optimal Control and Optimal Synthesis
- Sub-Riemannian geometry
- Feedback Equivalence and Feedback Invariants
- Switching Systems
- Quantum Control
- Systems Biology
- Control of Fluid Mechanics Systems
- Optimal Transportation
- Aplications to Vision and Robotics
- Applications to Differential Geometry and Dynamical Systems

Research Group:

## Geometric control

In this course (1 cycle), I will discuss the basic tools of geometric control theory. The program is the following:

## Geometric control theory

- Control systems on smooth manifolds; orbits and attainable sets.
- Linear systems: controllability test.
- Chronological calculus.
- Orbits theorem of Nagano and Sussmann
- Rashevskij-Chow and Frobenius theorems.
- Nagano equivalence principle.
- Control of configurations ("fallen cats").
- Structure of attainable sets; Krener's theorem.
- Compatible vector fields. Relaxation.
- Nonwandering points and controllability.

## Geometry and Control

## Research topics

- Optimal Control and Optimal Synthesis
- Sub-Riemannian geometry
- Feedback Equivalence and Feedback Invariants
- Switching Systems
- Quantum Control
- Control of Fluid Mechanics Systems
- Optimal Transportation
- Aplications to Vision and Robotics
- Applications to Differential Geometry and Dynamical Systems
- Stochastic Geometry
- Real algebraic Geometry