The underlying topic of this lecture is the development, analysis, and implementation of numerical algorithms for robust control and stabilization of (partial) differential equations. A particular focus lies on large-scale descriptor systems that play a role in the control of flows. Within the vast research field of numerical methods for control systems, we pursue the so-called H-infinity controller design that is designed to work even if the model is faulty.
After an introduction into the basic notions and principles of dynamical systems and control, I will address the challenges that come with high-dimensional (or even infinite-dimensional) nonlinear systems and show some recent theoretical and numerical approaches to their solution. The findings and concepts are illustrated by applications to the Navier-Stokes model equations and to a real-world triple pendulum.
If time suffices, I will address data-driven approaches that use data and possibly techniques from Machine Learning to enhance the models in terms of accuracy or faster evaluation times.