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Computer Science > Systems and Control

arXiv:1310.6481 (cs)
[Submitted on 24 Oct 2013]

Title:Barrier Certificates Revisited

Authors:Liyun Dai, Ting Gan, Bican Xia, Naijun Zhan
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Abstract:A barrier certificate can separate the state space of a con- sidered hybrid system (HS) into safe and unsafe parts ac- cording to the safety property to be verified. Therefore this notion has been widely used in the verification of HSs. A stronger condition on barrier certificates means that less expressive barrier certificates can be synthesized. On the other hand, synthesizing more expressive barrier certificates often means high complexity. In [9], Kong et al consid- ered how to relax the condition of barrier certificates while still keeping their convexity so that one can synthesize more expressive barrier certificates efficiently using semi-definite programming (SDP). In this paper, we first discuss how to relax the condition of barrier certificates in a general way, while still keeping their convexity. Particularly, one can then utilize different weaker conditions flexibly to synthesize dif- ferent kinds of barrier certificates with more expressiveness efficiently using SDP. These barriers give more opportuni- ties to verify the considered system. We also show how to combine two functions together to form a combined barrier certificate in order to prove a safety property under consid- eration, whereas neither of them can be used as a barrier certificate separately, even according to any relaxed condi- tion. Another contribution of this paper is that we discuss how to discover certificates from the general relaxed condi- tion by SDP. In particular, we focus on how to avoid the unsoundness because of numeric error caused by SDP with symbolic checking
Comments: 11 pages 5 figures
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:1310.6481 [cs.SY]
  (or arXiv:1310.6481v1 [cs.SY] for this version)
  https://doi.org/10.48550/arXiv.1310.6481

Submission history

From: Dai Liyun [view email]
[v1] Thu, 24 Oct 2013 04:31:12 UTC (162 KB)
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