   UHH > Fakultäten > MIN-Fakultät > Mathematik > Personen > Mathematical Systems and Control Theory WiSe 2019/20 STiNE |  KUS-Portal |    ## Mathematical Systems and Control Theory WiSe 2019/20

### General Information

The design of technical processes is often carried out by considering a model of the underlying dynamics, e.g. in the form of ordinary differential equations. This dynamics can often be influenced by actuators for controlling the solution of the differential equation. On the other hand, often one has only partial information on the dynamics of the system but only information by measurements. In this course we will analyze the resulting state-space systems in detail. In particular, we will study controllability and observability notions and discuss optimal control strategies. These tasks often lead to different types of matrix equations whose solution structure and numerical schemes are discussed.
• examples of state-space systems
• analysis of linear systems (controllability, stabilizability, observability, detectability)
• frequency domain analysis (Laplace transformation, Hardy spaces)
• stabilization, pole placement, and Lyapunov equations
• linear-quadratic optimal control and algebraic Riccati equations
• state estimation (Luenberger observer, Kalman filter)
• design of H and robust controllers (optional)

### Prerequisites

#### Required

• basic courses in linear algebra and calculus

#### Recommended

• basic course in optimization
• numerical analysis/numerical linear algebra

### Schedule

 Lecture: Monday, 4:15-5:45pm in Geom H5 Exercise: Wednesday, 4:15-5:45pm in Geom H6 (every even week, starting at October 30, 2019)

### Recommended Literature

 In this course I will try to prepare some lecture notes (based on lecture notes by Peter Benner). Further literature: K. Zhou, J. C. Doyle, and K. Glover. Robust and Optimal Control. Prentice-Hall, Englewood Cliffs, NJ, 1996. B. N. Datta. Numerical Methods for Linear Control Systems. Elsevier Academic Press, San Diego, CA, 2004.

### Exams

 Exams will be oral and of about 30 minutes length. They can be taken in English or German (your choice). The exact dates for the exam will be announced later.

### Exercises

Every student should at least present one solution on the blackboard.
 1st exercise sheet, discussion on October 30. 2nd exercise sheet, discussion on November 13. 3rd exercise sheet, discussion on November 27. 4th exercise sheet, discussion on December 11.  Impressum 2019-12-02, Mathematical Systems and Control Theory WiSe 2019/20