Examiner and lecturer:
Ulf Jönsson,
ulfj@math.kth.se ,
room 3711, Lindstedtsv 25, phone 790 8450
Tutorial exercises:
Johan Karlsson ,
johan.karlsson@math.kth.se ,
room 3737, phone 790 75 07.
Yohei Kuroiwa ,
yohei@math.kth.se ,
room 3727, phone 790 6660.
Introduction
This is an introductory course in mathematical systems theory. The
subject provides the mathematical foundation of modern control theory,
with application in aeronautics, electrical networks, signal
processing, and many other areas. The aim of the course is that you
should acquire a systematic understanding of linear dynamical systems,
which is the focus of this course. The acquirement of such knowledge
is not only very useful preparation for work on system analysis and
design problems that appear in many engineering fields, but is also
necessary for advanced studies in control and signal processing.
Course goals
The overall goal of the course is to provide an understanding of the
basic ingredients of linear systems theory and how these are used in
analysis and design of control, estimation and filtering systems. In
the course we take the state-space approach, which is well suited for
efficient control and estimation design. After the course you should
be able to
Course material
The required course material consists of the following lecture and exercise notes on sale at ``studentexpeditionen'' on Lindstedtsv 25
Course requirements
The course requirements consist of an obligatory final written
examination. There are also three optional homework sets, a computer
exercise, and an optional theory projects that we strongly encourage
you to do. All these activities will give you bonus credits in the
examination.
Homework sets
Each homework set consists of five problems. The first three are
methodology problems where you practice on the topics of the course
and apply them to examples. The last two problem are of more theoretical
nature and helps you to understand the mathematics behind the
course. It can, for example, be to derive an extension of a result in
the course or to provide an alternative proof of a result in the
course.
Each successfully completed homework set gives you maximally 3 points for
the exam. The exact requirements will be posted on each separate
homework set. The homework sets will be handed out in class roughly
two weeks before the deadline. They will also be posted on the course
homepage.
Computer exercise
The purpose of the computer exercises is to exemplify how easy it is
to apply the theory of the course using standard linear algebra
packages for numerical computations. We will use the ``Control System
Toolbox'' in MATLAB, for this purpose. The exercises serve the
additional purpose of applying the results of the course to two realistic
control problems.
The examination of the computer exercise is oral and written. Firstly
the results should be presented in a written report (approximately 5
pages written using Latex or Microsoft Word) and secondly each student
should be prepared to answer questions about the exercise when it is
handed back. Cooperation in groups of not more than two students is
allowed and only one report per group should be turned in. You should
mail your report to your project examiner. A successfully completed
computer exercise gives you three bonus points on the final exam.
Here is the exercise [pdf]. You may also use the following m-file [m].
The deadline for the report is on October 9, 2007 at 17.00. Attach your commented MATLAB code to your report!
Theory project
In the theory projects you will learn about new topics on linear
systems theory that are related to the course material. In this way
you learn how to develop the theory on your own.
The examination of each project is oral and written. Firstly the
results should be presented in a brief report and secondly each student
should be prepared to answer questions about the exercise when it is
handed back. Cooperation in groups of not more than two students is
allowed and only one report per group should be turned in. You should
mail your report to your project examiner. A successfully completed project
gives you three bonus points on the final exam. The following topics are
available (you should do one of them)
Written exam
This is an open book exam and you may bring the lecture notes 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 and the computer exercises (max credit is 115
points). These grade limits can only be modified to your advantage.
| Total credit (points) | Grade |
|---|---|
| 91-115 | A |
| 76-90 | B |
| 61-75 | C |
| 51-60 | D |
| 45-50 | E |
| 41-44 | FX |
Appeal
If your total score (exam score + maximum 15 bonus points from the
homework assignments and the computational exercises) is in the range 41-44
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
At the last tutorial exercise you will be asked to complete a course
evaluation form. The evaluation form will also be posted on the course
homepage and it can be handed in anonymously in the mailbox opposite
to the entrance of "studentexpeditionen" on Lindstedtsv 25. We
appreciate your candid feedback on lectures, tutorials, course
materials, homeworks and computer exercises. This helps us to
continuously improve the course.
Tentative schedule for 2007
| Type | Day | Date | Time | Hall | Instr | Topic |
|---|---|---|---|---|---|---|
| L1. | Fri | 31/8 | 15-17 | E33 | UJ | Introduction
|
| L2. | Tue | 4/9 | 15-17 | M23 | UJ | Linear systems
|
| L3. | Wed | 5/9 | 15-17 | D31 | UJ | Linear systems
|
| E1. | Thu | 6/9 | 15-17 | D41 | YK | Linear systems
|
| L4. | Fri | 7/9 | 15-17 | E32 | UJ | Reachability
|
| L5. | Tue | 11/9 | 10-12 | M22 | UJ | Reachability cont'd
|
| L6. | Wed | 12/9 | 15-17 | M33 | UJ | Observability
|
| L7. | Thu | 13/9 | 13-15 | M22 | UJ | Stability
|
| E2. | Tue | 18/9 | 15-17 | M31 | YK | Reachability and observability
|
| L8. | Wed | 19/9 | 15-17 | D41 | UJ | Realization theory and canonical forms
|
| L9. | Thu | 20/9 | 13-15 | M22 | UJ | Kalman decomposition and minimal realizations
|
| E3. | Fri | 21/9 | 15-17 | D41 | YK | Stability and realization theory
|
| L10. | Tue | 25/9 | 10-12 | E34 | UJ | Constructing minimal realizations
|
| E4. | Wed | 26/9 | 15-17 | D41 | YK | Realization theory
|
| L11. | Thu | 27/9 | 13-15 | M22 | JK | State feedback and observers
|
| E5. | Fri | 28/9 | 15-17 | D41 | JK | Pole assignment and observers
|
| L12. | Tue | 2/10 | 10-12 | E34 | UJ | Observers and observer based control.
|
| L13. | Wed | 3/10 | 15-17 | M23 | UJ | Linear quadratic control |
| L14. | Thu | 4/10 | 15-17 | D41 | UJ | The Riccati equation
|
| E6. | Fri | 5/10 | 15-17 | D41 | UJ | Linear quadratic control |
| L15. | Tue | 9/10 | 10-12 | M22 | UJ | Least squares estimation |
| L16. | Wed | 10/10 | 15-17 | M23 | UJ | Kalman filtering and the separation theorem |
| L17 . | Thu | 11/10 | 13-15 | UJ | Office hour | |
| E7. | Tue | 16/10 | 15-17 | M23 | JK | LQ, Kalman filtering, and the separation theorem |
| E8. | Wed | 17/10 | 15-17 | M22 | JK | LQ, Kalman filtering, and the separation theorem
|