Selected Methods for nonlinear Systems 1
Module EI7148
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.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 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.
- 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.
- 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
- 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).
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
- Tafelarbeit, Overhead
- Skript
- Simulationbeispiele während Vorlesung und Übung
- Übungsaufgaben mit Lösungen als Download im Internet
- Präsentationen
- Tafelarbeit, Overhead
- Skript
- Simulationbeispiele während Vorlesung und Übung
- Übungsaufgaben mit Lösungen als Download im Internet
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
K.J. Aström, Adaptive Control, Addison-Wesley Publishing,1995
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