Abstractions for hybrid systems

We present a procedure for constructing sound finite-state discrete abstractions of hybrid systems. This procedure uses ideas from predicate abstraction to abstract the discrete dynamics and qualitative reasoning to abstract the continuous dynamics of the hybrid system. It relies on the ability to decide satisfiability of quantifier-free formulas in some theory rich enough to encode the hybrid system. We characterize the sets of predicates that can be used to create high quality abstractions and we present new approaches to discover such useful sets of predicates. Under certain assumptions, the abstraction procedure can be applied compositionally to abstract a hybrid system described as a composition of two hybrid automata. We show that the constructed abstractions are always sound, but are relatively complete only under certain assumptions.