Stochastic systems

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

An understanding of model development and identification of stochastic systems. The course is devoted to large network systems, with the goal to develop skill in the prediction and control of traffic flow in such networks. Stochastic transport models are based on statistical data description with Bayesian rules.

Requirements:

Syllabus of lectures:

1.Models of traffic network - examples of simple model of traffic flow.

2.Least square (LSQ) method for static regressive model.

3.Matrix representation of LSQ method.

4.Dynamic programming of static regressive models.

5.Composite, marginal and conditional probability.

6.Discrete probabilistic models - representation by a table.

7.Continuous probabilistic models - represented by a probability density.

8.Prediction and identification in a continuous probability model.

9.Prediction and identification in a normal regressive model of order - n.

10.Prediction and identification in a discrete probability model with alternative distribution function.

11.Prediction and identification in a model with uniform distribution function.

12.Optimal control theory - Riccatti equation for probability density.

13.Control process under unknown model parameters- naive strategy.

14.Control process under unknown model parameters - careful strategy.

Syllabus of tutorials:

Study Objective:

Study materials:

Peterka V.: Bayesian approach to system identification, P. Eykhoff ed., Pergamon Press. Oxford, 1981

Eykhoff P.: System identification. Parameter and state estimation, John Wiley &Sons, 1974

Sivia D. S.: Data analysis: a Bayesian tutorial, Oxford Science Publications, 1996

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: