Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-33-M-7

Optimal Control of ODEs and DAEs (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-33-M-7 Optimal Control of ODEs and DAEs 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
+ 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


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-33-K-7
Optimal Control of ODEs and DAEs
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-33-K-7]: Title: "Optimal Control of ODEs and DAEs"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86343 ("Optimal Control of ODEs and DAEs")

Evaluation of grades

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


  • optimal control of ODEs and DAEs: introduction and examples,
  • infinite-dimensional optimization,
  • necessary optimality conditions,
  • numerical solution: indirect methods, direct methods, function-space methods,
  • optional topics: model-predictive control(MPC); dynamic programming; mixed-integer optimal control.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand basic concepts of optimal control, and they know examples of optimal control problems occurring in applications. They master concepts and methods needed for the analysis of such problems. Moreover, they are able to compare different approaches and methods for the numerical solution of such problems and to critically assess the possibilities and limitations for the applicability of the methods.

They have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.


  • M. Gerdts: Optimal Control of ODEs and DAEs,
  • J.T. Betts: Practical Methods for Optimal Control and Estimation using Nonlinear Programming,
  • L.S. Pontryagin, V.G. Boltyanskij, R.V. Gamkrelidze, E.F. Mishenko: Mathematische Theorie optimaler Prozesse,
  • A.D. Ioffe, V.M. Tihomirov: Theory of extremal problems,
  • A.E. Bryson, Y.-C. Ho: Applied Optimal Control.

References to Module / Module Number [MAT-81-33-M-7]

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