Optimal Control of Ordinary Differential Equations 2
Module MA5316
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 2012/3 | SS 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 workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 45 h | 5 CP |
Content, Learning Outcome and Preconditions
Content
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.
Preconditions
Required: MA3312 Optimal Control of Ordinary Differential Equations 1;
Recommended: MA2304 Numerical Methods for Ordinary Differential Equations, MA2005 Ordinary Differential Equations
Recommended: MA2304 Numerical Methods for Ordinary Differential Equations, MA2005 Ordinary Differential Equations
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Optimal Control of Ordinary Differential Equations II | Callies, R. |
Fri, 12:15–13:45, MI 00.09.022 |
eLearning |
| UE | 1 | Optimal Control of Ordinary Differential Equations II (Exercise Session) | Callies, R. |
Thu, 08:30–10:00, MI 03.06.011 |
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.
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.
Media
Blackboard and beamer
Literature
Bryson, Ho: Optimal Control.
Leitmann: The Calculus of Variations and Optimal Control.
Originalliteratur
Leitmann: The Calculus of Variations and Optimal Control.
Originalliteratur
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.