# Kontrolltheorie (Control Theory) - SoSe 2017

### Schedule:

The lecture will be in English (BMS course).

 Lecturer: Robert Altmann Lectures: Tue   12-14   in  MA 551 Wed   10-12   in  MA 549

### Exams:

There will be oral exams (~ 35 min) at the end of the semester.

• Thursday, September 7 (room MA 461)
• Monday, September 18 (room MA 461)

### Topics of the lecture:

• mathematical fundamentals in system and  control theory
• analysis of control systems: controllability, stabilizability, observability, reconstructability, detectability
• Lyapunov equations and stability theory
• optimal control problems
• algebraic Riccati equations

### Exercises:

There will be six exercise sheets (roughly every two weeks). Some parts will be distributed as written exercises, solutions will be discussed - mainly by the students - within the lectures.

### Lectures:

• 18.04: introduction, repetition (ODEs)
• 19.04: repetition (Laplace transform, SVD, invariant subspaces), inverted pendulum
• 25.04: control systems in frequency domain
• 26.04: discussion of 1. Exercise
• 02.05: controllability Gramian
• 03.05: controllability matrix, Kalman decomposition
• 09.05: Hautus-Popov lemma, stabilizability
• 10.05: discussion of 2. Exercise
• 16.05: reconstructability, observability
• 17.05: detectability, feedback equivalence
• 23.05: discussion of 3. Exercise
• 24.05: staircase form
• 30.05: Sylvester equation
• 31.05: Lyapunov equation
• 06.06: numerical solution of Lyapunov equations (Kronecker)
• 07.06: Bartels-Stewart
• 13.06: discussion of 4. Exercise
• 14.06: matrix sign function method, partial stabilization
• 20.06: pole placement I
• 21.06: pole placement II
• 27.06: --- no lecture ---
• 28.06: discussion of 5. Exercise
• 04.07: pole placement algorithms
• 05.07: optimal control with differential Riccati equation
• 11.07: algebraic Riccati equation
• 12.07: discussion of 6. Exercise
• 18.07: algorithm of Laub for solving the ARE
• 19.07: Newton method for solving the ARE

### Lecture notes:

 Impressum Robert Altmann 17.07.2017