The paper addresses the problem of synthesizing barrier certificates, which serve as differential invariants to witness system safety, for cyber-physical systems (CPS) defined over unbounded domains. Existing computational methods for barrier certificate synthesis are based on semidefinite programming (SDP) and rely on Putinar's Positivstellensatz, which is only applicable to bounded domains.
The authors first clarify the connection between the sound and complete sum-of-squares characterization of polynomial barrier certificates over bounded domains. They then propose two novel approaches to handle unbounded domains:
Polynomial Barrier Certificates:
Semialgebraic Barrier Certificates:
Experimental results on a set of benchmark systems demonstrate that the two complete characterizations are more effective at synthesizing barrier certificates over unbounded domains, compared to the existing incomplete approach.
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by Hao Wu,Sheng... kl. arxiv.org 04-29-2024
https://arxiv.org/pdf/2312.15416.pdfDybere Forespørgsler