Type-Based Verification of Delegated Control in Hybrid~Systems (Full Version)

We present a post-region-based verification system for distributed hybrid systems modeled with Hybrid Active Objects. The post-region of a class method is the region of the state space where a physical process must be proven safe to ensure some object invariant. Prior systems computed the post-region locally to a single object and could only verify systems where each object ensures its own safety, or relied on specific, non-modular communication patterns. The system presented here uses a type-and-effect system to structure the interactions between objects and computes post-regions globally, but verifies them locally. Furthermore, we are able to handle systems with delegated control: the object and method that shape the post-region change over time. We exemplify our approach with a model of a cloud-based hybrid system.