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Exponential-Condition-Based Barrier Certificate Generation for Safety Verification of Hybrid Systems

  • Hui Kong
  • Fei He
  • Xiaoyu Song
  • William N. N. Hung
  • Ming Gu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8044)

Abstract

A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinear hybrid systems. In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems. The most important benefit of Exponential Condition is that it has a lower conservativeness than the existing convex conditions and meanwhile it possesses the convexity. On the one hand, a less conservative barrier certificate forms a tighter over-approximation for the reachable set and hence is able to verify critical safety properties. On the other hand, the convexity guarantees its solvability by semidefinite programming method. Some examples are presented to illustrate the effectiveness and practicality of our method.

Keywords

inductive invariant barrier certificate safety verification hybrid system nonlinear system sum of squares 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hui Kong
    • 1
    • 2
    • 5
    • 6
  • Fei He
    • 2
    • 5
    • 6
  • Xiaoyu Song
    • 3
  • William N. N. Hung
    • 4
  • Ming Gu
    • 2
    • 5
    • 6
  1. 1.Dept. of Computer Science&TechnologyTsinghua UniversityBeijingChina
  2. 2.School of SoftwareTsinghua UniversityBeijingChina
  3. 3.Dept. of ECEPortland State UniversityOregonUSA
  4. 4.Synopsys IncMountain ViewUSA
  5. 5.Tsinghua National Laboratory for Information Science and TechnologyChina
  6. 6.Key Laboratory for Information System SecurityMOEChina

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