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Hybridization Based CEGAR for Hybrid Automata with Affine Dynamics

  • Nima RoohiEmail author
  • Pavithra Prabhakar
  • Mahesh Viswanathan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)

Abstract

We consider the problem of safety verification for hybrid systems, whose continuous dynamics in each mode is affine, \(\dot{X}=AX+b\), 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, \(\dot{x} \in \mathcal {I}\), where x is a variable and \(\mathcal {I}\) is an interval in \(\mathbb {R}\). 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 \(\mathtt {HARE}\) (Hybrid Abstraction-Refinement Engine), that makes calls to \(\mathtt {SpaceEx}\) 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, \(\mathtt {SpaceEx}\), \(\mathtt {PHAVer}\), \(\mathtt {SpaceEx~AGAR}\), and \(\mathtt {HSolver}\).

Notes

Acknowledgement

The authors would like to thank Sergiy Bogolomov for help with using the SpaceEx AGAR. We gratefully acknowledge the support of the following grants — Nima Roohi was partially supported by NSF CNS 1329991; Pavithra Prabhakar was partially supported by EU FP7 Marie Curie Career Integration Grant no. 631622 and NSF CAREER 1552668; and Mahesh Viswanathan was partially supported by NSF CCF 1422798 and AFOSR FA9950-15-1-0059.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Nima Roohi
    • 1
    Email author
  • Pavithra Prabhakar
    • 2
  • Mahesh Viswanathan
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignIllinoisUSA
  2. 2.Department of Computing and Information SciencesKansas State UniversityManhattanUSA

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