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Selected Methods for nonlinear Systems 2

Module EI7149

This Module is offered by TUM Department of Electrical and Computer Engineering.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

EI7149 is a semester module in English language at Master’s level which is offered in summer semester.

This module description is valid from WS 2009/10 to WS 2013/4.

Total workloadContact hoursCredits (ECTS)
90 h 45 h 3 CP

Content, Learning Outcome and Preconditions


In the summer term (part 2) geometrical tools for nonlinear systems design and analysis are presented. An introduction to differential geometry is provided with emphasis on dynamical systems defined on manifolds:
- what is a manifold?
- when is a global or local state space transformation possible (Frobenius Theorem)?
In particular, we underscore the fact that the natural state space of any nonlinear system is given by such a manifold ("curved space"). We discuss:
- the commutativity of vector fields,
- the Lie bracket,
- the notion of a distribution of a vector field and
- state Frobenius' theorem on integrability of distributions.
This insight is instrumental for designing intelligent and/or adaptive controllers for complex SISO/MIMO nonlinear systems. "Selected methods for nonlinear systems 1 and 2" are mainly independently from each other, hence part 1 is not obligatory for attendance of part 2.

Learning Outcome

At the end of this module students are able to:
- handle with and to understand manifolds,
- apply and to understand state space transformations (Frobenius Theorem),
- understand hamiltonian and lagragian systems,
- apply and use Lie-Brackets,
- understand, design and implement stable intelligent nonlinear (e.g. adaptive) controllers


Grundkenntnisse in:
- linearer Regelungstheorie
- Höhere Mathematik (Differentialgleichungen)

Folgende Module sollten vor der Teilnahme bereits erfolgreich absolviert sein:

Es wird empfohlen, ergänzend an folgenden Modulen teilzunehmen:
- Dynamic Systems

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

Als Lernmethode wird zusätzlich zu den individuellen Methoden des Studierenden eine vertiefende Wissensbildung durch mehrmaliges Aufgabenrechnen in Übungen angestrebt.

Als Lehrmethode wird in Vorlesungen und Übungen Frontalunterricht gehalten, in den Übungen auch Arbeitsunterricht (Aufgaben rechnen, Diskussion und Analyse realitätsnaher Problemstellungen z.B. anhand von Simulationsbeispielen, Lösungsansätze bewerten und hinterfragen).


Folgende Medienformen finden Verwendung:
- Präsentationen
- Tafelarbeit, Overhead
- Skript
- Simulationbeispiele während Vorlesung und Übung
- Übungsaufgaben mit Lösungen als Download im Internet


M. Vidyasagar, Nonlinear System Analysis, SIAM Classics in Applied Mathematics, 2002
S. Narendra, Stable Adaptive Systems, Prentice Hall, 1989
J.-J. E. Slotine, Applied Nonlinear Control, Prentice Hall, 1991
A. Isidori, Nonlinear Control Systems, Springer, 1995
K.J. Aström, Adaptive Control, Addison-Wesley Publishing,1995

Module Exam

Description of exams and course work

Modulprüfung mit folgenden Bestandteilen: - Abschlussklausur
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