Stochastic Control Theory 2016

Graduate course, FRT055F

Lecturer: Björn Wittenmark


PhD course in Stochastic Control Theory based on Karl Johan Åström (2006): Introduction to Stochastic Control Theory, Dover Publications. (The first edition of the book was published by Academic Press in 1970.) There will be nine lectures/seminars covering different aspects of stochastic control both continuous-time and discrete-time. The main emphasis is, however, on the discrete-time case. The course is open for all PhD students and gives 7.5 ECTS credits.

Preliminary Schedule

  • Monday January 18, 13:15-15:00
  • Wednesday January 20, 10:15-12:00
  • Monday January 25, 13:15-15:00
  • Wednesday January 27, 10:15-12:00
  • Wednesday February 17, 10:15-12:00
  • Wednesday February 24, 10:15-12:00
  • Wednesday March 2, 10:15-12:00
  • Wednesday March 9, 10:15-12:00
  • Monday March 14, 13:15-15:00
  • Wednesday March 16, 10:15-12:00

Course Material (subject to change)

1 Introduction, fundamental definitions KJÅ 1,2 Assignment 1
2 Stochastic state-space models 1 KJÅ 3 Assignment 2
3 Stochastic state-space models 2 KJÅ 3 Assignment 3
4 Analysis KJÅ 4 Assignment 4
5 Parametric optimization KJÅ 5 Assignment 5
6 Prediction and filtering KJÅ 7 Assignment 6
7 LQG in state-space form KJÅ 8 Assignment 7
8 Prediction and minimum variance control in polynomial form, Extra slides CCS 12 Assignment 8
9 LQG in polynomial form. Wiener filter Link 1 Link 2

Assingment 9

10 Guest lecture by Karl Johan Åstöm, KJÅ part 1, KJÅ part 2, and Anton Cervin, Jitterbug    


Good examples

There is a list of good examples from Åström: Introduction to Stochastic Control to practice your skills on.


Solutions to examples are available by courtesy from Tore Hägglund.


Some corrections to Åström: Introduction to Stochastic Control.


Ahlén, A. and M. Sternad (1991): "Wiener filter design using polynomial equations", IEEE Trans. on Signal Processing, SP-39, 2387-2399

Åström, K. J. (1970): Introdiction to Stochastic Control Theory, Academic Press

Åström, K. J. and B. Wittenmark (1971): "Problems of identification and control", Journal of Mathematical Analysis and Applications, 34, 90-113

Åström, K. J. and B. Wittenmark (1997): Computer-Controlled Systems, 3rd ed., Prentice Hall

Kalman, R. E. (1960): "A new approach to linear filtering and prediction problems", ASME J. Basic Eng., 82, 35-45

Levinson, N. (1947): "The Wiener RMS (Root Mean Square) error criterion in filter design and prediction", in Wiener, N: Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press, 129-148

Söderström, T.(2002): Discrete-time Stochastic Systems, 2nd ed., Springer Verlag