Graduate course

Stochastic dynamic systems, winter/spring 2009


I will give a graduate course on Stochastic dynamic systems during February - May 2009.
The course will start in mid-February. Precise details will be announced later on
this web page. The course will be given in English.


As a text we will use my  book
T. Söderström: Discrete-Time Stochastic Systems -- Estimation and Control.
Second edition, Springer-Verlag, 2002.
Errata for the second edition.


The course should be appropriate for graduate students in automatic control,
signal processing, systems theory, mathematical statistics, engineering disciplines, physics, etc.

It is assumed that the participants have some basic working knowledge in
stationary stochastic processes, linear algebra, and  discrete-time dynamic systems.
A MSc (civilingenjör) in engineering physics or an equivalent background from another
undergraduare program should be sufficient.
This also means that senior undergraduate students in their final year can
sufficient background, and will be welcome to participate.


There will be a session of 4 hours a week. Each session will include

The students will be given regular homework problems to be solved.
This will be a part of the examination.


The homework problems will be an essential part of the examination.
There will also be a final 'take-home' exam.
The homeworks assignments are organized into two parts, A and B.
Part A is mandatory, while the exercises in part B can be done by students
who wants a deeped experience in the field (and more credit point).
The basic alternatives are thus

If there is an interest from undergraduate students to take a smaller
course, I will be open to discuss such an option.


In order to plan the schedule for the course,
I would like interested participants to register for the course as soon as possible,
and not later than by January 30, 2009.
You can do so by contacting  me: phone (018-183075),  or email.
Please let me know if you have specific desires concerning
the schedule.

Course plan
Session Week Chapter Topics Homeworks
1 8 1-3 Introduction. probability theory.
Complex-valued Gaussian variables.
Stochastic processes.
2 9 3-4 Second and higher order moments.
Linear filtering. 
A: 2:1, 3
B: 2: 4
State space representations.
Linear filtering. Spectral factorization
A: 3:3
B: 3:6

11 4 Continuous-time models. Sampling.
Positive real part of the spectrum.
A: 3: 1
B: 3: 4

12 4 Bispectrum and filtering.
Algorithms for covariance calculations.
A: 4: 1, 2, 3
B: 4: 17

13 5 Optimal estimation. A: 4: 4, 8
B: 4: 6, 18

14 6 Optimal state estimation of linear systems
(Kalman filters).
A: 4: 12, 19
B: 4: 11

16 7 Optimal estimation of linear systems using
a polynomial approach
(Wiener filters).
A: 5: 1, 3
B: 5: 2

17 9 Nonlinear filtering.
(Extended Kalman filtering, quantisation, medians).
A: 6: 7, 8, 15
B: 6: 17, 20

18 10 Optimal stochastic control.
Dynamic programming.
A: 7: 1, 9
B: 7: 3
19 11 Linear quadratic Gaussian (LQG) control.
Duality. Controller design.
A: 9: 3,  8
B: 9: 13
  General discussion. A: 10: 1, 4, 
     11: 5, 8
B: 10: 2, 
     11: 7

Schedule and venue

The sessions are normally scheduled for Mondays 13.15 - 17.
Then venue is room P2345 (in house 2, MIC).

There are a few exceptions:
week 8: The session for this week is on Tuesday (February 17), 13.15-17.
week 15: Note that there is likely no session this week.
week 16: The session for this week is on Tuesday (April 14), 13.15-17.
week 21: Monday May 18 is booked as a reserve time.

OH slides in postscript:

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 9
Chapter 10
Chapter 11

Department of Systems and Control, Uppsala University | URL
Last updated: 08 January 2009 by Torsten Söderström