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Geometric control

Lecturer: 
Ugo Boscain
Course Type: 
PhD Course
Academic Year: 
2016-2017
Period: 
April-May
Duration: 
20 h
Description: 

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

  • Definition of control systems on  smooth manifolds. Feedback. Families of vector fields. Differential inclusions. The classical problems in geometric control: controllability, stabilizability, optimal control.
  • The controllability problem: the Kalman condition for Linear systems, the Krener Theorem, the Chow Theorem. Compatible vector fields: Systems with recurrent drift, systems satisfying the strong Hormander condition.
  • The problem of finding a smooth stabilizing feedback. The Brockett condition.
  • Optimal control: the Filippov theorem; the Pontryagin Maximum Principle; minimum time for linear systems. Minimum time for 2D non-linear systems. Systems with quadratic cost.
  • Extensions: Connection to problem of sub-Riemannian geometry. What happens if we put in place of the control a Brownian motion.
Location: 
Lecture of June 1st in Room 005.

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