Abstract
With the rapid increase in data resources and computational power as well as the accompanying current trend to incorporate machine learning into existing methods, data-driven approaches for modelling, analysis, and control of dynamical systems have attracted new interest and opened doors to novel
applications.
However, there is always a discrepancy between mathematical models and reality such that rigorously-shown error bounds and uncertainty quantification are indispensable for a reliable use of data-driven techniques, e.g., using surrogate models in optimisation-based control. Similar comments apply to data-enhanced models.
Consequently, uncertainty about parameters, the model itself and numerous other aspects need to be taken into account, e.g., in data-driven control of (stochastic) dynamical systems.
Hence, the respective paradigm changes have led to a variety of novel concepts which, however, still suffer from limitations: many concentrate only on a single aspect, are only applicable to systems of limited complexity, or lack a sound mathematical foundation including guarantees on feasibility, robustness, or the overall performance.
Pushing these limits, we face a wide spectrum of theoretic
and algorithmic challenges in modeling, analysis, and control under uncertainty using data-driven methods.