# Chair of Dynamics and Control

# Main topics at a glance

## Holder of Chair

Stefan Siegmund received his doctorate in mathematics from the University of Augsburg in 1999. After research stays in the USA at the Georgia Institute of Technology in Atlanta, the Institute for Mathematics and Its Applications at the University of Minnesota in Minneapolis, the University of California at Berkeley and the Boston University, he was head of an Emmy Noether Research Group at the Goethe University in Frankfurt before he was appointed professor at TU Dresden in 2008.

## Research

Interesting models e.g. in biology, physics, meteorology often lead to or are approximated by finite-dimensional dynamical systems which depend on parameters. For which parameters does the system bifurcate and change its dynamical behavior? For which model classes can we describe and control the dynamical behavior although the model is only partly known? Every applied question leads to interesting mathematical problems and often to new concepts…

## TEACHING

In addition to german Bachelor calculus and advanced calculus lectures we regularly offer lectures on dynamical systems and control theory (Math Ma DYSYSG & DYSYSV), as well as research seminars on various levels. If you are not sure whether you are satisfying the prerequisites and want to learn more about the recommended prior knowledge of our master lectures you can take a look at the lecture overview. It is also possible to write your master thesis in english...

# Why dynamics and control?

A **dynamical system** is a rule for time evolution on a state space, e.g. the

- locations and speeds of planets in a solar system described by Newton’s law „force = mass x acceleration“, or the
- motion of billiard balls on a billiard table.

Dynamical systems are generated e.g. by the solutions of ordinary deterministic or random differential equations, difference equations, iterated function systems, cellular automata, dynamic equations with time delay, differential algebraic equations and many more. Dynamical systems are semigroup actions, usually of the non-negative reals or integers, on a manifold which is often a subset of a Banach space.

**Control theory** studies systematically the controllability of the time evolution of states under constraints, e.g. the

- reachability of stable orbits of satellites with a prescribed amount of fuel, or the
- development of a heat control which stabilizes the room temperature.

Control systems are e.g. differential equations which depend on a control which can be chosen from a set of admissible functions. Laplace transforms for the analysis in the frequency domain and Lyapunov functions from stability theory are used to develop a mathematical control strategy which can then be implemented in a real system.