Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-82-11-M-7

Numerical Methods in Control Theory (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-82-11-M-7 Numerical Methods in Control Theory 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-82-11-K-7
Numerical Methods in Control Theory
P 56 h 214 h - - PL1 9.0 irreg.
  • About [MAT-82-11-K-7]: Title: "Numerical Methods in Control Theory"; Presence-Time: 56 h; Self-Study: 214 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86330 ("Numerical Methods in Control Theory")

Evaluation of grades

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


Contents

Numerical methods dealing with problems of the linear control theory will be covered, especially:
  • general and structured eigenvalue problems, normal forms,
  • matrix equations (e.g. Lyapunov and Riccati) and their numerical solutions,
  • general theory of huge systems of equations,
  • reduction of model (especially based on singular value decompositions and Krylov subspace method).

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand basic concepts for the numerical treatment of control problems as well as the mathematical techniques to analyze these methods. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

With the help of concrete exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture. They have learnt how to apply the methods to new problems, analyze them and develop solution strategies.

Literature

  • A.C. Antoulas: Approximation of Large-Scale Dynamical Systems,
  • P.H. Petkov, N.D. Christov, M.M. Konstantinov: Computational Methods for Linear Control Systems,
  • B. Datta: Numerical Methods for Linear Control Systems,
  • A. Linnemann: Numerische Methoden für lineare Regelungssysteme,
  • K. Zhou, J.C. Doyle, K. Glover: Robust and Optimal Control.

References to Module / Module Number [MAT-82-11-M-7]

Module-Pool Name
[MAT-82-MPOOL-7] Specialisation Systems and Control Theory (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)