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Geometric Control Theory and Sub-Riemannian Geometry

  • 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

Introduction to geometric control

The course of 10 lectures will provide an introduction to geometric control theory. The first part of the course will be devoted to controllability, the second part will discuss stabilization, while the last part will focus on optimal control. No prior knowledge of control theory is required.

Course program:
1. Some basic questions in the control formalism, some examples of control systems.
2. Controllability of linear systems. Lie brackets and their relation with controlled motions.

Geometric control

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


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