Mixed first-principles and data-integrated modeling for control

This project aims at developing rigorous approaches for integrating first principles with input-output data for representing dynamical systems, as well as their use for system-theoretic analysis and controller synthesis. We will link classical model structures with function approximation techniques from state-of-the-art machine learning and develop these into suitable methods for mixed modeling and control with learning capabilities. Bayesian nonparametric approaches such as Gaussian process regression are one promising direction as the Bayesian formalism allows for the systematic combination of prior knowledge (such as first principles) and data, and for quantifying uncertainty. In a second thrust, we will research data-based or model-free control, which represents the dynamical system directly through trajectory data. The developed methods will be demonstrated on data from both simulation and physical hardware. The developed modeling tools are closely linked to system-theoretic analysis developed in PN 4-2 and will be used for controller synthesis in PN 4-3.