Safety Verification of Piecewise-Deterministic Markov Processes

Rafael Wisniewski, Christoffer Sloth, Manuela Bujorianu, Nir Piterman

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

7 Citations (Scopus)


We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set of initial states from which the probability to reach designated unsafe states is at most 1-p. Based on the knowledge of the full generator of the PDMP, we are able to develop a system of partial differential equations describing the connection between unsafe and initial states. We then show that by using the moment method, we can translate the infinite-dimensional optimisation problem searching for the largest set of p-safe states to a finite dimensional polynomial optimisation problem. We have implemented this technique on top of GloptiPoly and show how to apply it to a numerical example.
Original languageEnglish
Title of host publicationHSCC '16 Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control
PublisherAssociation for Computing Machinery
Publication date2016
ISBN (Print)978-1-4503-3955-1
Publication statusPublished - 2016
Event8th Cyber Physical Systems Week (CPS Week): 19th ACM International Conference on Hybrid Systems: Computation and Control - Vienna, Austria
Duration: 12 Apr 201614 Apr 2016


Conference8th Cyber Physical Systems Week (CPS Week)


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