U. Boscain
SISSA
Optimal Synthesis and Applications to Quantum Mechanics (``un ciclo'')
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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.
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| Bidimensional minimum time problems.
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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).
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| Introduction to Quantum Mechanics.
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Finite dimensional quantum problems.
- Elimination of the drift.
- Reduction to real problems.
- The choice of the cost.
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The key example: 3-level systems
- Resonance.
- Minimizing the energy.
- Minimizing time with bounded controls.
- The STIRAP strategy.
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