Stochastic Control Theory

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.

Planning meeting Tuesday January 11 at 9.15.

Lectures Tuesday 8.15 - 10.00, in the seminar room of the department starting February 8, 2011.

Schedule Tuesday 8.15 - 10.00

January 11 Planning meeting
February 8 Introduction, fundamental definitions KJÅ 1,2 Assignment 1
February 15 Stochastic state-space models 1 KJÅ 3 Assignment 2
February 22 Stochastic state-space models 2 KJÅ 3 Assignment 3, Assignment 3.2
March 1 Analysis KJÅ 4 Assignment 4
March 8 Parametric optimization KJÅ 5 Assignment 5
March 15 Prediction and filtering KJÅ 7 Assignment 6
March 29 LQG in state-space form KJÅ 8 Assignment 7
April 5 Prediction and minimum variance control in polynomial form CCS 12 Assignment 8
April 12 LQG in polynomial form. Wiener filter Link 1 Link 2
Assingment 9


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


One-day-exam to be done before Friday May 13, 2011.