KTH /
Engineering Science
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Mathematics
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Optimization and Systems Theory
SF2842 Geometric Control Theory
Examiner and lecturer
Xiaoming Hu
(hu@math.kth.se),
Room 3532, Lindstedtsv. 25, tel. 790 7180.
Teaching assistant
Yuecheng Yang
(yuecheng@math.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
Course requirements
The course requirements consist of an obligatory final written
examination. There are also three homework sets we strongly encourage
you to do. All these optional activities will not only give you bonus
credits in the examination, but also help you understand the course
material better.
Homework
Each homework set consists of not more than five problems. Each successfully completed
homework set gives you maximally 5 points for
the exam. 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.
Note: The date in parentheses is the last day
(before 5 pm) for handing in the
written solutions. The homework questions will be made available online
about ten days before the deadline.
2015 Homework and solution:
Written exam
Written exam will be compulsory from V16.
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, where the total score is the sum of
your exam score and maximally fifteen bonus points from the homework
assignments (max credit is 115
points). These grade limits can only be modified to your advantage.
Total credit (points)  Grade


>90  A
 7690  B
 6175  C
 5060  D
 4549  E
 4144  FX

The grade FX means that you are allowed to make an appeal, see below.
The first exam will take place on March 21, 2016 at 08:0013:00.
Solutions to exam of March 21, 2016 can be found here.
Appeal
If your total score (exam score + maximum 15 bonus points from the
homework assignments) is in the range 4144
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 2016
F=Lecture, E=Exercise
Type  Day  Date  Time  Hall  Topic


F1.  Wed  20/01  1315  D32
 Introduction
 F2.  Thu  21/01  1012  D32
 Invariant subspaces
 F3.  Fri  22/01  1315  D41
 Invariant subspaces (cont.)
 E1.  Mon  25/01  1517  D32
 Linear algebra, invariant subspaces
 F4.  Wed  27/01  1315  D42
 Disturbance decoupling
 F5.  Thu  28/01  1012  L21
 Disturbance decoupling, and Zeros
 F6.  Mon  1/02  1517  D32
 Zeros and zero dynamics (cont.)
 E2.  Wed  3/02  1315  E33
 Reachability subspaces, V*algorithm, zero dynamics
 F7.  Thu  4/02  1012  E53
 Zero dynamics and high gain control
 F8.  Mon  8/02  1517  E53
 Noninteracting control and tracking
 F9.  Wed  10/02  1315  D42
 Inputoutput behavior
 E3.  Thu  11/02  1012  L22
 Applications of zero dynamics
 F10.  Mon  15/02  1517  E53
 Inputoutput behavior and Output regulation
 F11.  Wed  17/02  1315  E53
 Output regulation (cont.)
 E4.  Thu  18/02  1012  E53
 Sylvester equation, Output tracking input, Output regulation
 F12.  Mon  22/02  1517  E33
 Nonlinear systems: examples, math preparation
 F13.  Wed  24/02  1315  D42
 Nonlinear systems: controllability, stability
 F14.  Thu  25/02  1012  E53
 Nonlinear systems: steady state response
 F15.  Mon  29/02  1517  D32
 Center manifold and normal form
 E5.  Wed  2/03  1315  D42
 Nonlinear systems
 F16.  Thu  3/03  1012  E53
 Nonlinear systems: zero dynamics and applications
 F17.  Mon  7/03  1517  D32
 Exact linearization and Consensus problem
 F18.  Wed  9/03  1315  E53
 Multiagent systems
 E6.  Thu  10/03  1012  D32
 Nonlinear control and multiagent systems

Welcome!
