A Train Protection Logic Based on Topological Manifolds for Virtual Coupling

Virtual coupling is a promising innovation aimed at increasing railway capacity. Compared to current railway signaling systems, it allows two or more trains to run with reduced headway between them. However, such reduced headways are a challenge to safety. In this work we consider this challenge by formally describing and verifying an approach to virtual coupling. We propose a general modeling method based on topological manifolds to describe the protection logic for virtual coupling train control systems. We also describe the basic train control elements in topological terms and analyze the line condition of our virtual coupling logic. We establish that the line condition safety requirements and its representation as a manifold are equivalent and further provide a formal definition of the concept of a movement authority with manifold notations. This allows us to consider the dynamic behavior of trains and a series of theorems that establish the correctness of our protection logic for virtual coupling. Finally, we apply the presented methods to a case study. The results show that the proposed method provides a suitable way to realize a virtual coupling logic safely.