Talk of Prof. Fritz Colonius

March 25, 2024

--- Title: Chain Controllability of Linear and Affine Systems

Time: March 25, 2024
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Prof. Dr. Fritz Colonius
Institute of Mathematics
 University of Augsburg
Augsburg, Germany  


Monday 2024-03-25 2 p.m.
IST Seminar Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen



This talk concerns controllability properties of affine control systems described by ordinary differential equations with bounded controls. Here controllability in the state space is an exceptional property, but controllability in subsets will hold. I will discuss chain controllability properties which constitute a weaker version of approximate controllability and may be difficult to distinguish from it in numerical computations. Here small jumps in the trajectories are allowed and hence this is not a physical notion. The characterization of chain control sets reveals, in particular, the linear nature of chain control sets, despite the presence of control constraints. The first part of the talk will discuss linear systems, and the second part presents the main results for affine systems.


Biographical Information

After the study of mathematics in Braunschweig and Bielefeld, Fritz Colonius obtained his doctoral degree (1979) and habilitation (1986) from the University of Bremen. Following various postdoc positions (including at the University of Graz and Brown University) and a Heisenberg grant he held a position as Professor for Applied Analysis at the University of Augsburg till his retirement in 2017.
After early work on functional differential equations, optimal periodic control, and parameter identification problems, he has mainly worked on various aspects of nonlinear systems theory and its relations to deterministic and random dynamical systems.

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