An Approach to Proving Proof Obligation of Hybrid Event B Based on Differential Invariants

For modelling hybrid systems, we have extended Event B based on its framework with the differential event. The differential event describes continuous behaviors of hybrid systems by differential equations and evolution constraint, whose proof obligations provide dynamical properties of a model. In order to ensure the safety and reliability of a model, proof obligations should be proved. It is difficult to prove proof obligation in state space, because there is no a complete method to solve differential equations in the field of mathematics. Thus we proposed an approach to proving proof obligation based on differential invariants. It is to avoid uncontrollable computation on solving differential equation. The main result is that we prove some theorems for proving proof obligations involving differential events within the framework of refinement calculus. Lastly, through the case of the Train Control System, we further show that the approach is well suited.