Dario Prandi bio photo

Dario Prandi

Researcher in control theory and biomimetic image processing.

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Graduate course of the master PDE and scientific calculus of the University Paris-Sud Orsay

Period: Winter semester 2013/2014

10h of Travaux Dirigé (teaching assistantship) and 10h of tutoring

Material:

Topics of the course:

  • Controllability:
    • Definition of control systems as families of dynamical systems
    • Structural properties
    • Accessibility, controllability and stabilization
    • Lie bracket, the Lie algebraic condition and the Brockett obstruction
    • Krener theorem, Chow theorem, the orbit theorem
    • Controllability for systems under the strong Hörmander condition and with unbounded controls
    • The Frobenius Theorem
  • Optimal Control:
    • The classical approach of the calculus of variations (Euler-Lagrange equations)
    • Legendre transform and the Hamiltonian formalism
    • Existence of solutions: Filippov Theorem
    • Pontryagin Maximum Principle
    • Singular trajectories and abnormal extremals
    • Sub-Riemannian geometry and the hypoelliptic Laplacian