Lecturer:
Course Type:
PhD Course
Academic Year:
2017-2018
Period:
October-February
Duration:
60 h
Description:
- Vector fields and control systems. Lie brackets.
- Linear systems: controllability, optimization, normal forms.
- Elements of the chronological calculus.
- Intrinsic characterization of linear systems.
- Orbits and attainable sets. Nagano, Sussmann, and Krener theorems.
- Applications: control of rigid and liquid bodies.
- Feedback (gauge) transformations.
- Relaxation technique: “hidden convexity”.
- Optimal control problem. Existence of solution.
- Elements of symplectic geometry and Pontryagin Maximum Principle.
- Some model optimal control problems: a particle on the line, oscillator, Markov–Dubins and Euler interpolation problems.
- Fields of extremals and sufficient optimality conditions.
- Optimal cost: Hamilton–Jacobi–Bellmann equation.
- Second variation, conjugate points and Jacobi equation.
- Singular extremals: Goh and generalized Legendre conditions.
- The chattering phenomenon.
- Curvature of optimal control problems.
Reference:
A. Agrachev, Yu. Sachkov, Control theory from the geometric viewpoint. Springer, 2004
Location:
A-133