Proving hybrid systems

Abstract

Cyber-physical systems (CPS) combine cyber aspects such as communication and computer control with physical aspects such as movement in space, which arise frequently in many safety-critical application domains, including aviation, automotive, railway, and robotics. But how can we ensure that these systems are guaranteed to meet their design goals, e.g., that an aircraft will not crash into another one? This tutorial focuses on the most elementary CPS model: hybrid systems, which are dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. It describes a compositional programming language for hybrid systems and shows how to specify and verify correctness properties of hybrid systems in differential dynamic logic. Extensions of this logic that support CPS models with more general dynamics will be surveyed briefly. In addition to providing a strong theoretical foundation for CPS, differential dynamic logics have also been instrumental in verifying many applications, including the Airborne Collision Avoidance System ACAS X, the European Train Control System ETCS, several automotive systems, mobile robot navigation with the dynamic window algorithm, and a surgical robotic system for skull-base surgery. The approach is implemented in the theorem prover KeYmaera X.