Graduate course

Stochastic dynamic systems, winter/spring 2003


Schedule

I will give a graduate course on Stochastic dynamic systems during February - May 2003.
The course will start in mid-February. Precise details will be announced later on
this web page. The course will be given in English.

Literature

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.

Prerequisites

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.

Organisation

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.

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.

Registration

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 31, 2003.
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
3
 10
 4
 State space representations.
Linear filtering. Spectral factorization
 A: 3:3
B: 3:6
4

 11 4 Continuous-time models. Sampling.
Positive real part of the spectrum.		 A: 3: 1
B: 3: 4
5

 12 4 Bispectrum and filtering.
Algorithms for covariance calculations.		 A: 4: 1, 2, 3
B: 4: 17
6

 13 5 Optimal estimation. A: 4: 4, 8
B: 4: 6, 18
7

 14 6 Optimal state estimation of linear systems
(Kalman filters).		 A: 4: 12, 19
B: 4: 11
8

 15 7 Optimal estimation of linear systems using
a polynomial approach
(Wiener filters).		 A: 5: 1, 3
B: 5: 2
9

 17 9 Nonlinear filtering.
(Extended Kalman filtering, quantisation, medians).		 A: 6: 7, 8, 15
B: 6: 17, 20
10

 18 10 Optimal stochastic control.
Dynamic programming.		 A: 7: 1, 9
B: 7: 3
11
 19 11 Linear quadratic Gaussian (LQG) control.
Duality. Controller design.		 A: 9: 3,  8
B: 9: 13
12
 20
 		  General discussion. A: 10: 1, 4, 
     11: 5, 8
B: 10: 2, 
     11: 7

Schedule and venue

The sessions are scheduled for Mondays 13.15 - 17.
Then venue is room 8127 (in house 8, MIC).

There are a few exceptions:
week 16: Note that there is no session.
week 17: The session for this week is on Tueday (April 22), 13.15-17.
week 20: This session will be on May 12, 13.15-17, in room 8105.
 

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 http://www.SysCon.uu.se
Last updated: 11 September 2003 by Torsten Söderström