Mathematical Systems and Control Theory

Period 1 & 2

Level: 400

COURSE OBJECTIVE
The course aims to introduce the student to the mathematical theory of control systems.

COURSE CONTENT
Many phenomena are characterized by dynamic behaviour where we are interested in a certain input/output behaviour. Examples are to be found in the exact and natural sciences (mechanics, biology, ecology), in engineering (air- and spacecraft design, mechanical engineering) as well as in economics and econometrics (macro- economical models, trend and seasonal influences in demand and supply, production systems). Systems theory is concerned with modeling, estimation and control of dynamical phenomena. During the course the following subjects will be treated: models and representations (linear systems, input-output, state space, transfer function, stochastic systems, spectrum), control (stabilisation, feedback, pole placement, dynamic programming, the LQ problem), and identification and prediction (parameter estimation, spectral analysis, Kalman- filter, model reduction). Applications are in the area of optimal control and prediction.

TEACHING METHODS
There is a lecture of two hours each week. In addition, there is another session which will be half lecture and half practicum, in which there is the possibility to ask questions about the compulsary computerpracticum. The practicum makes use of the Matlab package.

TYPE OF ASSESSMENT
The computerpracticum counts for 50%, the oral examination concerns the theory and counts for 50%.

RECOMMENDED BACKGROUND KNOWLEDGE
Analysis, probability theory, statistics. Complex analysis and Fourier theory would be useful, but are not absolutely necessary.