Graduate course

Stochastic dynamic systems, fall 2015


Schedule

I will give a graduate course on Stochastic dynamic systems during September - December 2015. The course will start in mid-September. 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.

Organisation

There will be two sessions of 4 hours every second 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 deepened experience in the field (and more credit points). The basic alternatives are thus


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 September 4, 2015. You can do so by contacting me by email.

Preliminary Course plan
 
Session Week Day
 Chapter Topics
 
  Homeworks    
   
1 38 Mon
14/9
1-3 Introduction. probability theory.
Complex-valued Gaussian variables.
Stochastic processes.		  
2 38 Thu
17/9
 3-4 Second and higher order moments.
Linear filtering. 		 A: 2:1, 3
3
 41
 Mon
5/10
 4
 State space representations. Linear filtering. Spectral factorization
 A: 3:3
B: 2: 4
4
 41
 Thu
8/10
 4 Continuous-time models. Sampling. Positive real part of the spectrum. A: 3: 1
B: 3:6
5
 43 Mon
19/10
 4 Bispectrum and filtering.
Algorithms for covariance calculations.		 A: 4: 1, 2, 3
B: 3: 4, 4: 17
6
 43
 Thu
22/10
 5 Optimal estimation. A: 4: 4, 8
B: 4: 6, 18
7
 45 Mon
2/11
 6 Optimal state estimation of linear systems (Kalman filters). A: 4: 12, 19
B: 4: 11
8
 45
 Thu
5/11
 7 Optimal estimation of linear systems using a polynomial approach
(Wiener filters).		 A: 5: 1, 3
B: 5: 2
9

 47
 Mon
16/11
 9 Nonlinear filtering.
(Extended Kalman filtering, quantization, medians).		 A: 6: 7, 8, 15, 7: 1
B: 6: 17, 20
10
 47
 Thu
19/11
 10 Optimal stochastic control.
Dynamic programming.		 A: 7: 9, 9: 8
B: 7: 3
11
 49
 Mon
30/11
 11 Linear quadratic Gaussian (LQG) control. Duality. Controller design. A: 9: 3, 10: 1, 4
B: 9: 13, 10: 2
12
 49
 		Thu
3/12
   General discussion. A: 11: 5, 8
B: 11: 7

Schedule and venue

The sessions are normally scheduled for Mondays and Thursdays 13.15 - 17. The venue is room P2344 (in house 2, MIC).

The take-home exam will be scheduled later for one week in the period Week 50.

OH slides in postscript:

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


 
Last updated: 14 April 2015 by Torsten Söderström