## Abstrakt

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.

Originalsprog | Engelsk |
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Titel | Proceedings of the 19th International Conference on Hybrid Systems : Computation and Control |

Antal sider | 10 |

Forlag | Association for Computing Machinery |

Publikationsdato | 11. apr. 2016 |

Sider | 257-266 |

ISBN (Elektronisk) | 9781450339551 |

DOI | |

Status | Udgivet - 11. apr. 2016 |

Udgivet eksternt | Ja |

Begivenhed | 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016 - Vienna, Østrig Varighed: 12. apr. 2016 → 14. apr. 2016 |

### Konference

Konference | 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016 |
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Land/Område | Østrig |

By | Vienna |

Periode | 12/04/2016 → 14/04/2016 |

Sponsor | ACM Special Interest Group on Embedded Systems (ACM SIGBED) |