Hybridization Based CEGAR for Hybrid Automata with Affine Dynamics

We consider the problem of safety verification for hybrid systems, whose continuous dynamics in each mode is affine, Ẋ = AX + b, and invariants and guards are specified using rectangular constraints. We present a counter-example guided abstraction refinement framework (CEGAR), which abstract these hybrid automata into simpler ones with rectangular inclusion dynamics, ẋ ∈ I, where x is a variable and I is an interval in R. In contrast to existing CEGAR frameworks which consider discrete abstractions, our method provides highly efficient abstraction construction, though model-checking the abstract system is more expensive. Our CEGAR algorithm has been implemented in a prototype tool called HARE (Hybrid Abstraction-Refinement Engine), that makes calls to SpaceEx to validate abstract counterexamples. We analyze the performance of our tool against standard benchmark examples, and show that its performance is promising when compared to state-of-the-art safety verification tools, SpaceEx, PHAVer, SpaceEx AGAR, and HSolver.