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Optimal control

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2020-2021
Period: 
October - January
Duration: 
60 h
Description: 

1. Control systems and optimal control problems.
2. Linear systems. Controllability and the energy minimization problem.
3. Vector fields, flows and Lie brackets. Elements of the chronological calculus.
4. Orbits and attainable sets. Nagano–Sussmann and Krener theorems.
5. Relaxation techniques and hidden convexity.
6. Existence of optimal control.
7. Elements of symplectic geometry and Pontryagin Maximum Principle.
8. Some model optimal control problems: a particle on the line, oscillator, Markov–Dubins and Euler interpolation problems.
9. Linear time-optimal problem.
10. Fields of extremals and sufficient optimality conditions.
11. Optimal cost: Hamilton–Jacobi–Bellmann equation.
12. Second variation, conjugate points and Jacobi equation.
13. Singular extremals: Goh and generalized Legendre conditions.
14. Bang-bang extremals: discrete Jacobi equation.
15. The chattering phenomenon.
16. Curvature of optimal control problems.

Reference:

A. Agrachev, Yu. Sachkov, Control theory from the geometric viewpoint. Springer, 2004

Location: 
A-133
Next Lectures: 
Tuesday, October 27, 2020 - 11:00 to 13:00
Wednesday, October 28, 2020 - 11:00 to 13:00
Tuesday, November 3, 2020 - 11:00 to 13:00
Wednesday, November 4, 2020 - 11:00 to 13:00
Tuesday, November 10, 2020 - 11:00 to 13:00
Wednesday, November 11, 2020 - 11:00 to 13:00
Tuesday, November 17, 2020 - 11:00 to 13:00
Wednesday, November 18, 2020 - 11:00 to 13:00
Tuesday, November 24, 2020 - 11:00 to 13:00
Wednesday, November 25, 2020 - 11:00 to 13:00
Tuesday, December 1, 2020 - 11:00 to 13:00
Wednesday, December 2, 2020 - 11:00 to 13:00
Wednesday, December 9, 2020 - 11:00 to 13:00
Tuesday, December 15, 2020 - 11:00 to 13:00
Wednesday, December 16, 2020 - 11:00 to 13:00
Tuesday, December 22, 2020 - 11:00 to 13:00
Wednesday, December 23, 2020 - 11:00 to 13:00
Tuesday, January 12, 2021 - 11:00 to 13:00
Wednesday, January 13, 2021 - 11:00 to 13:00
Tuesday, January 19, 2021 - 11:00 to 13:00
Wednesday, January 20, 2021 - 11:00 to 13:00
Tuesday, January 26, 2021 - 11:00 to 13:00
Wednesday, January 27, 2021 - 11:00 to 13:00

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