Nonlinear Control

Module number: MW1808

Duration: 1 Semester

Recurrence: Winter semester

Language: English

Number of ECTS: 5


Professor in charge: PD Dr.-Ing. habil. Paul Kotyczka

Amount of work

Class attendance: 45

Private Study: 105

Total: 150

Course work and exam formalities

In a written exam (90min.) the contents of the module are evaluated. The exam consists of short theoretical questions (approx. 1/3, a part of them formulated as multiple choice questions) and problems involving calculations in the style of the exercises (approx. 2/3).


- State space representation and analysis of nonlinear dynamical systems.

- Equilibria and stability. Lyapunov's methods. Passivity.

- Different nonlinear controller design techniques will be discussed:

feedback Linearization (Input-/Outpunt, Input-/state)

Flatness based feedforword control


Passivity based control

Flatness based feedforward control

- An introduction into differential geometric concepts for nonlinear control is given

Learning outcome

At the end of the lecture the students are able to:

- analyze important properties of nonlinear system like stability of equilibria and passivity

- applyflatness based feedforward control

- develop nonlinear controllers based on: feedback lineariation, backstepping, passivity arguments

- understand the idea of adaptive control and apply MRCA

- understand the optimization based rationale behind model predictive control


A course about linear state feedback design, e.g. Advanced Control


The lecture will be written on the blackboard and supplemented with slides and handouts. Exercises and their solutions as well as addditional material will be available for download.


The lecture is self-contained. However, the following textbooks are recommended for the interested reader:

Slotine, J.-J. E., Li, W.: Applied Nonlinear Control, Prentice-Hall, 1991.

Khalil, H.: Nonlinear Systems, Prentice Hall, 1196.

Teaching and studying methods

Weekly courses: 90 min. lecture, 45 min. exercise course, 45 min. additional exercise course (optional). Exercises and their solutions will be available for download.

In addition, for interested students, an optional 45 min. session is offered to discuss advanced topics and clarify questions which go beyond the scope the lecture.