This website is no longer updated.

As of 1.10.2022, the Faculty of Physics has been merged into the TUM School of Natural Sciences with the website For more information read Conversion of Websites.

de | en

Optimal Control of Ordinary Differential Equations 2

Module MA5316

This Module is offered by TUM Department of Mathematics.

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.

Module version of WS 2012/3 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2012/3SS 2012

Basic Information

MA5316 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from SS 2011 to WS 2018/9.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Necessary conditions of higher order (e.g. Legendre-Clebsch, Jacobi), state constraints, bang-bang and singular control, sufficient conditions, application problems

Learning Outcome

After successful completion of the module students are able to formulate and analyze optimal control problems for ordinary differential equations subject to contraints and to transform them in a way suitable for numerical treatment.


Required: MA3312 Optimal Control of Ordinary Differential Equations 1;
Recommended: MA2304 Numerical Methods for Ordinary Differential Equations, MA2005 Ordinary Differential Equations

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

Lecture with integrated exercise
In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.


Blackboard and beamer


Bryson, Ho: Optimal Control.
Leitmann: The Calculus of Variations and Optimal Control.

Module Exam

Description of exams and course work

Depending on the number of students, the examination is either oral or a 60 minutes' written test without any auxiliary resources. The students are asked to explain important facts and sketch the corresponding proofs and derivations of the content of the lecture listed above. Moreover, they have to solve a typical benchmark problem. With that they demonstrate that they have fully understood the main ideas of the lecture and are able apply that knowledge to application problems.

Exam Repetition

The exam may be repeated at the end of the semester.

Top of page