Safe learning and control in complex systems

When autonomously controlling physical objects, a deviation from a trajectorycan lead to unwanted impacts, which can be very expensive or even dangerous. Thedeviation may be due to uncertainties, either from disturbance or model mismatch.One way to deal with these types of uncertainties is to design a robust control sys-tem, which creates margins for errors in the system. These margins make the systemsafe but also lowers the performance, hence it is desirable to have the margins assmall as possible and still make the system safe. One way to reduce the margins isto add a learning strategy to the control system, which improves the model repre-sentation using previous data. In this thesis, we investigate a robust control systemcalled tube-based model predictive control and then combine it with an adaptivegain scheduling method as the learning strategy. The adaptive feature in the gainscheduling method reduces the model mismatch between the model representationand the true dynamics by tuning the control parameters in the gain schedule usinga data-driven framework. To test this design, a dot is controlled to follow a pathin a constrained environment, around an obstacle. The dot should complete thetrack repeatedly without violating any constraints or crash into the obstacle whilereducing the model mismatch. Our results show that the error from the modelmismatch decreases with time without the dot touching the obstacle or moving out-side the constraints. As the error decreases, the margins in the controller becomesmaller, which makes it possible to control the system in a more efficient way andstill guarantee that the system remain safe