Hybrid Abstractions that Preserve Timed Languages

In this paper we consider the problem of extracting an abstraction from a hybrid control system while preserving timed languages. Such consistent abstractions are clearly useful as the abstracted, higher level model could be used for controller synthesis or verification of the more complicated lower level model. The class of abstracting maps we consider in this paper compress only the continuous states without aggregating any discrete states. Given such an abstracting map, we determine natural conditions that determine when trajectories of the original hybrid system can be generated by the abstracted hybrid system. Conversely, we determine conditions under which the two hybrid systems generate exactly the same timed language.