Lecturer:
Course Type:
PhD Course
Academic Year:
2003-2004
Period:
Academic year
Duration:
40 h
Description:
- 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.
Research Group: