Safe active learning control with Gaussian processes

In Project P4, we develop a novel framework for safe active learning in Gaussian process (GP) models used in learning-based control. GP regression offers a highly flexible machine learning method for learning nonlinear functions - specifically, uncertain dynamics - based on training data. It provides a principled approach to uncertainty quantification, which is crucial for ensuring robust guarantees. We will explore different notions of safety, including robust convergence and forward invariance. The main innovation of this project is the focus on active learning for control, which necessitates a different strategy from existing active learning methods for function regression, as indicated by our preliminary results. To this end, we will develop novel control-oriented data informativity measures, which will be used for exploration with guaranteed improvement rates in control performance. Additionally, computational aspects will be investigated. The developed algorithms will undergo theoretical analysis concerning robust control guarantees, learning rates, and uncertainty complexity trade-offs. Furthermore, they will be evaluated in the benchmark problems developed within the Research Unit ALeSCo.