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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

Lecturer

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.

 
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