Exponential-Condition-Based barrier certificate generation for safety verification of hybrid systems

  • Authors:

  • Hui Kong;Fei He;Xiaoyu Song;William N. N. Hung;Ming Gu

  • Affiliations:

  • Dept. of Computer Science&Technology, Tsinghua University, Beijing, China,School of Software, Tsinghua University, Beijing, China,Tsinghua National Laboratory for Information Science and Techn ...;School of Software, Tsinghua University, Beijing, China,Tsinghua National Laboratory for Information Science and Technology, China,Key Laboratory for Information System Security, MOE, China;Dept. of ECE, Portland State University, Oregon;Synopsys Inc, Mountain View, California;School of Software, Tsinghua University, Beijing, China,Tsinghua National Laboratory for Information Science and Technology, China,Key Laboratory for Information System Security, MOE, China

  • Venue:
  • CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
  • Year:
  • 2013

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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.