Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-80-18-M-4

Introduction to Systems and Control Theory & Dynamical Systems (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-80-18-M-4 Introduction to Systems and Control Theory & Dynamical Systems 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-80-12A-K-4
Introduction to Systems and Control Theory
P 42 h 93 h
U-Schein
- PL1 4.5 SuSe
2V+1U MAT-80-17-K-6
Dynamical Systems
P 42 h 93 h
U-Schein
- PL1 4.5 irreg. SuSe
  • About [MAT-80-12A-K-4]: Title: "Introduction to Systems and Control Theory"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-12A-K-4]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
  • About [MAT-80-17-K-6]: Title: "Dynamical Systems"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-17-K-6]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84265 ("Introduction to Systems and Control Theory; Dynamical Systems")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Basic terms and ideas of Systems and Control Theory as well as their applications will be discussed. In particular, the following contents will be covered:
  • representation of time-discrete and continuous linear and non-linear dynamic systems,
  • stability of dynamic systems,
  • accessibility, controllability, observability,
  • feedback rule.
  • basics: existence and uniqueness,
  • autonomous equations,
  • stability theory,
  • nonlinear systems, local theory, theorem of Hartman-Grobman, non hyperbolic equilibrium points and Lyapunov theory,
  • periodic orbits, Poincaré Bendixon and applications, invariant sets,
  • bifurcation theory,
  • applications.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the basic concepts required for describing dynamic systems as well as mathematical techniques for the analysis of these systems and the design of control systems. Furthermore, they are familiar with the various possible applications resulting from the use of mathematical control theory.

They have studied methods for qualitative treatment of dynamic systems and are able to apply them. The focus is on the behavior of solutions of ordinary differential equations under the influence of varying parameters in a system. The techniques taught are very useful for the study of nonlinear partial differential equations and control theory as well as for the study of practical problems that are modeled by using differential equations.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They are able to comprehend and explain the propositions and proofs presented in the lectures. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • E. Zerz: Introduction to Systems and Control Theory,
  • J.W. Polderman, J. Willems,: Introduction to Mathematical Systems Theory,
  • H.W. Knobloch, H. Kwakernaak, Lineare Kontrolltheorie,
  • D. Hinrichsen, A.J. Pritchard, Mathematical Systems Theory I,
  • E.D. Sontag, Mathematical Control Theory.
  • J.K. Hale, H. Kocak: Dynamics and Bifurcations,
  • H. Heuser: Gewöhnliche Differentialgleichungen,
  • B. Marx, W. Vogt: Dynamische Systeme,
  • J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme.
  • K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure. Band III: Gewöhnliche Differentialgleichungen, Distributionen, Integraltransformationen.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance of the module (informal)

Modules:

Courses

Requirements for attendance of the module (formal)

None

References to Module / Module Number [MAT-80-18-M-4]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective