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Optimal Synthesis and Applications to Quantum Mechanics

Course Type: 
PhD Course
Academic Year: 
Academic year
40 h
  • Introduction
    • Pontryagin Maximum Principle.
    • Abnormal extremals and Singular Trajectories.
    • What is a solution to an Optimal Control Problem?
    • Definition of Optimal Synthesis.
    • Comparison with the concept of feedback.
  • Bidimensional minimum time problems.
  • The Pontryagin Maximum Principle on Lie groups.
    • Trivialization of the cotangent bundle.
    • PMP on Lie groups.
    • Invariants
    • The K+P Problem.
    • Example: SL(2) (wave fronts, spheres, cut and conjugate loci).
  • Introduction to Quantum Mechanics.
  • Finite dimensional quantum problems.
    • Elimination of the drift.
    • Reduction to real problems.
    • The choice of the cost.
  • The key example: 3-level systems.
    • Resonance.
    • Minimizing the energy.
    • Minimizing time with bounded controls.
    • The STIRAP strategy.
Next Lectures: 

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