Professor Fritz Colonius
The Department is delighted to welcome Professor Fritz Colonius as Nelder Fellow in 2018.
Control Theory and Dynamical Systems
Fritz Colonius will present a series of lectures on "Control Theory and Dynamical Systems". Control theory has deep roots in engineering prob- lems shaping this interdisciplinary field which mainly involves engineers and mathematicians. A focus of the lectures will be on the interplay between dynamical systems theory and control-theoretic problems. A large class of control systems define continuous skew product flows and problems like con- trollability are closely related to topological mixing and chain transitivity. The spectral theory of linear skew product flows gives insight into stabiliz- ability and robustness. Furthermore, it will be shown how problems of control via digital channels under communication constraints lead to the emerging field of invariance and estimation entropy in control.
Lecture outline (6 Lectures of 50 minutes)
- Introduction to control
- Controllability and observability
- Control sets and the control flow
- Spectral theory for bilinear systems
- Invariance entropy and control under communication constraints
After early work on functional differential equations, optimal periodic control and parameter identification problems, Fritz Colonius has mainly worked on various aspects of nonlinear systems theory and its relations to de- terministic and random dynamical systems. The monograph "The Dynamics of Control", Birkhauser (2000), coauthored with Wolfgang Kliemann, was an acme of this research lying the foundations for much further work. His recent interests include control under information constraints, aspects of piecewise deterministic Markov processes and quasi-stationary measures.