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Geometric control theory

Lecturer: 
Andrei Agrachev
Course Type: 
PhD Course
Academic Year: 
2012-2013
Period: 
November-February
Duration: 
60 h
Description: 
  1. Control systems on smooth manifolds; orbits and attainable sets.
  2. Linear systems: controllability test.
  3. Chronological calculus.
  4. Orbits theorem of Nagano and Sussmann
  5. Rashevskij-Chow and Frobenius theorems.
  6. Nagano equivalence principle.
  7. Control of configurations ("fallen cats").
  8. Structure of attainable sets; Krener's theorem.
  9. Compatible vector fields. Relaxation.
  10. Nonwandering points and controllability.
  11. Controllability for Galerkin approximations of the Euler's ideal fluid equation.
  12. Optimal control problem. Existence of solution.
  13. Pontryagin Maximum Principle.
  14. Solution of model problems: a particle on the line, oscillator, Dubins car.
  15. Linear time-optimal problems.
  16. Linear-quadratic problems.
  17. Fields of extremals and sufficient optimality conditions.     
Location: 
A-133

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