Safety and transition-structure preserving abstraction of hybrid systems with inputs/outputs

We present a method for obtaining a discrete abstraction of a hybrid system modeled as an input-output hybrid automaton (I/O-HA), generalizing our earlier work on linear hybrid automaton with no inputs or outputs. The discrete abstraction we present preserves the discrete behaviors (the set of state trajectories sampled at instances immediately after the discrete transitions) of an I/O-HA, and thus it is adequate for safety verification. (The violation of a safety property can be formulated as the reachability of certain discrete states.) We represent the discrete behaviors of an I/O-HA as the discrete behaviors of an input-output transition system (I/O-TS), which possesses no continuous dynamics, i.e., it is a purely discrete system. A feature of our discrete abstraction of an I/O-HA into an I/O-TS is that it preserves the transition structure of the discrete dynamics, making it unique compared to the prior works on discrete abstraction of a hybrid system (which either did not preserve the discrete behaviors or the transition structure of the discrete dynamics). The discrete abstraction can be used for further analysis (such as verification, testing, control, diagnosis, monitoring, etc.) involving safety properties. The abstraction is illustrated through an adaptive cruise control example.