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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

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

  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.

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

 

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