Probably Approximate Safety Verification of Hybrid Dynamical Systems

  • Bai XueEmail author
  • Martin Fränzle
  • Hengjun Zhao
  • Naijun Zhan
  • Arvind Easwaran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11852)


In this paper we present a method based on linear programming that facilitates reliable safety verification of hybrid dynamical systems subject to perturbation inputs over the infinite time horizon. The verification algorithm applies the probably approximately correct (PAC) learning framework and consequently can be regarded as statistically formal verification in the sense that it provides formal safety guarantees expressed using error probabilities and confidences. The safety of hybrid systems in this framework is verified via the computation of so-called PAC barrier certificates, which can be computed by solving a linear programming problem. Based on scenario approaches, the linear program is constructed by a family of independent and identically distributed state samples. In this way we can conduct verification of hybrid dynamical systems that existing methods are not capable of dealing with. Some preliminary experiments demonstrate the performance of our approach.


Hybrid systems Probably approximately safe Linear program 



Bai Xue was funded by CAS Pioneer Hundred Talents Program under grant No. Y8YC235015, NSFC under grant No. 61872341 and 61836005. Martin Fränzle was funded by Deutsche Forschungsgemeinschaft through grant FR 2715/4. Hengjun Zhao was funded by NSFC under grant No. 61702425. Naijun Zhan was funded by NSFC under grant No. 61625206 and 61732001. Arvind Easwaran was supported by the Energy Research Institute (ERI@N), NTU, Singapore.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Bai Xue
    • 1
    • 2
    • 3
    Email author
  • Martin Fränzle
    • 4
  • Hengjun Zhao
    • 5
  • Naijun Zhan
    • 1
    • 2
  • Arvind Easwaran
    • 6
  1. 1.State Key Laboratory of Computer ScienceInstitute of Software, CASBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Beijing Institute of Control EngineeringBeijingChina
  4. 4.Carl von Ossietzky Universität OldenburgOldenburgGermany
  5. 5.Southwest UniversityChongqingChina
  6. 6.Nanyang Technological UniversitySingaporeSingapore

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