# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Prof. Dr. Volker
Mehrmann**, Institut für Mathematik, Technische Universität Berlin,
will give a public talk (followed by a discussion) on **Thu, Jan. 16, 2014**
at **14:00 o'clock** at **S2 416**
on the topic of
"Optimal control of flow problems via the discretization of transfer operators"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Optimal control of flow problems via the discretization of transfer operators

In the practical approach to optimal control of non-stationary partial

differential-equations, a typical procedure is to first discretize the

forward problem, then to carry out a model order reduction and to

perform the optimization on the reduced order model. Although this works

very well for many parabolic problems, it quickly gets to its limits due

to the costs of the model reduction process. In classical control

engineering, instead one uses a small surrogate model that is produced

from measured input/output data via a realization and applies the

optimal control in a feedback look or other local approaches. In this

talk we present a concept that uses a direct Galerkin/Petrov Galerkin

discretization of the input/output map that can be adapted to the

behavior of the transfer operator to obtain reduced order models and to

use in optimal control of flow problems. We present some analytic

results that show that in this way the error between space, time and

transfer operator discretization can be balanced and present several

numerical examples of successful applications of this technique.