Linking Discrete and Continuous Models, Applied to Traffic Manoeuvrers

The interplay between discrete and continuous dynamical models is discussed, and a systematic approach to developing and combining these models together is outlined. The combination is done with linking predicates that define refinement relations between the models. As a case study, we build an abstract, discr spatial model and a concrete, continuous dynamic model for traffic manoeuvrers of multiple vehicles on highways. In the discrete model we show the safety (collision freedom) of distance keeping and lane-change manoeuvrers using events and actions to specify state transitions. By linking the discrete and continuous model via suitable predicates that express the discrete events and actions as distances and set-points in the continuous model, the safety carries over to the concrete model.