All the lectures and exercises will take place live on Zoom. The respective Zoom ID's are:

Lectures: https://kth-se.zoom.us/j/66927112583. Meeting ID: 66927112583 Recorded lectures

Exercises: https://kth-se.zoom.us/j/61281827900.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.

Homework 1 (due February 8)
Homework 2 (due February 22)
Homework 3 (due March 8)

2020 Homework and solution:

Homework 1
Homework 2
Homework 3

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, 2021 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 2021

L=Lecture, E=Exercise

Type	Day	Date	Time	Hall	Topic
L1.	Mon	18/01	10-12	Zoom	Introduction
L2.	Tue	19/01	8-10	Zoom	Invariant subspaces
L3.	Wed	20/01	15-17	Zoom	Invariant subspaces (cont.)
E1.	Mon	25/01	10-12	Zoom	Linear algebra, invariant subspaces
L4.	Tue	26/01	8-10	Zoom	Disturbance decoupling
L5.	Wed	27/01	15-17	Zoom	Disturbance decoupling, and Zeros
L6.	Thu	28/01	8-10	Zoom	Zeros and zero dynamics (cont.)
E2.	Mon	1/02	10-12	Zoom	Reachability subspaces, V*-algorithm, zero dynamics
L7.	Tue	2/02	8-10	Zoom	Zero dynamics and high gain control
L8.	Thu	4/02	8-10	Zoom	Noninteracting control and tracking
E3.	Mon	8/02	10-12	Zoom	Applications of zero dynamics
L9.	Tue	9/02	8-10	Zoom	Input-output behavior
L10.	Wed	10/02	15-17	Zoom	Input-output behavior and Output regulation
L11.	Thu	11/02	8-10	Zoom	Output regulation (cont.)
E4.	Tue	16/02	8-10	Zoom	Sylvester equation, Output tracking input, Output regulation
L12.	Wed	17/02	15-17	Zoom	Nonlinear systems: examples, math preparation
L13.	Thu	18/02	8-10	Zoom	Nonlinear systems: controllability
L14.	Mon	22/02	10-12	Zoom	Nonlinear systems: Stability, steady state response
L15.	Tue	23/02	8-10	Zoom	Center manifold and normal form
E5.	Wed	24/02	15-17	Zoom	Nonlinear systems
L16.	Fri	26/02	8-10	Zoom	Nonlinear systems: zero dynamics and applications
L17.	Tue	2/03	8-10	Zoom	Exact linearization and Consensus problem
E6.	Wed	3/03	15-17	Zoom	Nonlinear control and multi-agent systems

Welcome!

SF2842 VT21 (60033) Geometric Control Theory