Reachability and Learning for Hybrid Systems

Hybrid systems allow for the composition of continuous and discrete state dynamics, and have been used in aircraft flight management, air and ground transportation systems, robotic vehicles and human-automation systems. These systems use discrete logic to manage complexity and more naturally accommodate linguistic and qualitative information. In this talk, we will present reachable set methods for controller design to satisfy safety specifications, and we will present a toolbox of methods combining reachability with machine learning techniques, to enable performance improvement while maintaining safety. We will illustrate these "safe learning" methods on UAV applications.