SF2842 Geometric Control Theory
All the lectures and exercises in January will take place live on Zoom.
The respective Zoom ID's are:
Lectures: https://kth-se.zoom.us/j/66927112583 Links to an external site.. Meeting ID: 66927112583
Exercises: https://kth-se.zoom.us/j/61281827900 Links to an external site.. Meeting ID: 61281827900
Examiner and lecturer
Xiaoming Hu (hu@math.kth.se), Room 3532, Lindstedtsv. 25, tel. 790 7180.
Teaching assistant
Yibei Li (yibei@kth.se), Lindstedtsv. 25, tel. 790 7132.
Course registration
Important! pleae read here for information on course registration and exam application.
Course contents
The goal of the course is to give students good knowledge about the fundamental results in the geometric control theory. Here is an introduction to the course.
Course material
- X. Hu, A. Lindquist et al, Geometric Control Theory, lecture notes, KTH, 2012, can be downloaded here:
Table of contents, Chapter one, Chapter two, Chapter three, Chapter four, Chapter five
Chapter six, Chapter seven, Chapter eight, Chapter nine, Appendix and index - Exercise notes:
Exercise 1, Exercise 2, Exercise 3, Exercise 4, Exercise 5, Exercise 6 - More information can be found here, a detailed solution to an old exam
Course requirements
The course requirements consist of an obligatory final written examination, and three homework sets.
Homework
Each homework set consists of not more than five problems. Each successfully completed homework set gives you 0.5hp. The exact requirements will be posted on each separate homework set. The homework sets will be posted roughly ten days before the deadline on the course homepage under assignments.
2020 Homework and solution:
Written exam
This is an open book exam and you may bring the lecture notes, the exercise notes, your own classnotes and Beta Mathematics Handbook (or any equivalent handbook). The exam will consist of five problems that give maximally 100 points. These problems will be similar to those in the homework assignments and the tutorial exercises. The preliminary grade levels are distributed according to the following rule. These grade limits can only be modified to your advantage.
| Total credit (points) | Grade |
|---|---|
| >84 | A |
| 71-84 | B |
| 56-70 | C |
| 46-55 | D |
| 40-45 | E |
| 35-39 | FX |
The grade FX means that you are allowed to make an appeal, see below.
- The first exam will take place on March 15, 2022 at 14:00-19:00.
Solutions to exam of March 2020 can be found here.
Appeal
If your score is in the range 35-39 points then you are allowed to do a complementary examination for grade E. In the complementary examination you will be asked to solve two problems on your own. The solutions should be handed in to the examiner in written form and you must be able to defend your solutions in an oral examination. Contact the examiner no later than three weeks after the final exam if you want to do a complementary exam.
Course evaluation
All the students are encouraged to answer the questionnaire on KTH Social.
Preliminary Schedule for 2022
L=Lecture, E=Exercise
| Type | Day | Date | Time | Hall | Topic |
|---|---|---|---|---|---|
| L1. | Wed | 19/01 | 10-12 | Zoom | Introduction |
| L2. | Thu | 20/01 | 10-12 | Zoom | Invariant subspaces |
| L3. | Fri | 21/01 | 10-12 | Zoom | Invariant subspaces (cont.) |
| E1. | Mon | 24/01 | 10-12 | Zoom | Linear algebra, invariant subspaces |
| L4. | Wed | 26/01 | 15-17 | Zoom | Disturbance decoupling |
| L5. | Thu | 27/01 | 13-15 | Zoom | Disturbance decoupling, and Zeros |
| L6. | Fri | 28/01 | 10-12 | Zoom | Zeros and zero dynamics (cont.) |
| E2. | Mon | 31/01 | 15-17 | Zoom | Reachability subspaces, V*-algorithm, zero dynamics |
| L7. | Wed | 2/02 | 15-17 | Zoom | Zero dynamics and high gain control |
| L8. | Thu | 3/02 | 13-15 | Zoom | Noninteracting control and tracking |
| L9. | Mon | 7/02 | 8-10 | Zoom | Input-output behavior |
| E3. | Wed | 9/02 | 15-17 | Zoom | Applications of zero dynamics |
| L10. | Thu | 10/02 | 13-15 | Zoom | Input-output behavior and Output regulation |
| L11. | Fri | 11/02 | 15-17 | Zoom | Output regulation (cont.) |
| L12. | Wed | 16/02 | 15-17 | B22 | Nonlinear systems: examples, math preparation |
| E4. | Thu | 17/02 | 13-15 | B22 | Sylvester equation, Output tracking input, Output regulation |
| L13. | Fri | 18/02 | 15-17 | B22 | Nonlinear systems: controllability |
| L14. | Mon | 21/02 | 8-10 | B22 | Nonlinear systems: Stability, steady state response |
| L15. | Wed | 23/02 | 15-17 | B22 | Center manifold and normal form |
| E5. | Thu | 24/02 | 13-15 | B25 | Nonlinear systems |
| L16. | Fri | 25/02 | 15-17 | B22 | Nonlinear systems: zero dynamics and applications |
| L17. | Mon | 28/02 | 13-15 | B24 | Exact linearization and Consensus problem |
| E6. | Thu | 3/03 | 15-17 | B24 | Nonlinear control and multi-agent systems |
Welcome!