Reachability and Learning for Hybrid Systems

Hybrid systems are a modeling tool allowing for the composition of continuous and discrete state dynamics. They can be represented as continuous systems with modes of operation modeled by discrete dynamics, with the two kinds of dynamics influencing each other. Hybrid systems have been essential in modeling a variety of important problems, such as aircraft flight management, air and ground transportation systems, robotic vehicles and human-automation systems. These systems use discrete logic in control because discrete abstractions make it easier to manage complexity and discrete representations more naturally accommodate linguistic and qualitative information in controller design. A great deal of research in recent years has focused on the synthesis of controllers for hybrid systems. For safety specifications on the hybrid system, namely to design a controller that steers the system away from unsafe states, we will present a synthesis and computational technique based on optimal control and game theory. We will briefly review these methods and their application to collision avoidance and avionics design in air traffic management systems, and networks of manned and unmanned aerial vehicles. Then, 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 a quadrotor UAV experimental platform which we have at Berkeley.