# 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

Date | Subject | Reference | Assignment |
---|---|---|---|

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

Solutions to examples are available by courtesy from Tore Hägglund.

## Corrections

Some corrections to Åström: Introduction to Stochastic Control.

## Literature

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

## Exam

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