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# Selected Methods for nonlinear Systems 1

## Module EI7148

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

EI7148 is a semester module in English language at Master’s level which is offered in winter semester.

This module description is valid from WS 2009/10 to SS 2011.

90 h 45 h 3 CP

### Content, Learning Outcome and Preconditions

#### Content

In the winter term (part 1) analytical methods for nonlinear control system design and analysis are introduced:
- description of nonlinear dynamical system by nonlinear ordinary differential equations (ODEs).
- their properties and requirements on the right hand side of the ODE are discussed to ensure e.g. existence and uniqueness of the solution,
- possible equilibrium points and the existence of periodic orbits. With that in mind, several stability criteria in the sense of Lyapunov are presented and tools for nonlinear control design are deduced (e.g. control Lyapunov functions). "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 the module students are able to:
- understand and analyse nonlinear ordinary differential equations and remember the difference to linear differential equations
- evaluate and analyse ODEs, e.g. such that a unique and maximal solution can be obtained or stability properties with the help of Lyapunov's 1. and 2. method can be deduced
- understand and distinguish between equilibria and periodic orbits.
- create and design stable intelligent nonlinear and/or adaptive controllers for nonlinear complex SISO/MIMO systems described by nonlinear ordinary differential equations.

#### Preconditions

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).

#### Media

Folgende Medienformen finden Verwendung:
- Präsentationen
- Skript
- Simulationbeispiele während Vorlesung und Übung

#### Literature

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