Mathematical Systems and Control Theory

COURSE OBJECTIVE
After completion of this course the student

1. has knowledge of the theory of finite dimensional linear systems, in particular in state space form, including the concepts and characterizations of observability, controllability, minimality of state space representations, and can apply this knowledge,

2. can design a dynamic feedback compensator for a give state space system, as well as a linear quadratic controller,

3. has knowledge of, and can apply several models for stochastic systems as well as stochastic realization theory and basic results on system identification,

4. can construct a Kalman filter for given data and

5. can apply his/her knowledge of systems and control theory with the aid of Matlab

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 dynamicalphenomena. 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
There are five sets of exercises, which together count for 40%. The individual final examination concerns the theory and counts for 60%. The final examination may be either a written exam or an oral examination, depending on the size of the group.

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