## Abstract

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 language | English |
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Title of host publication | Proceedings of the 19th International Conference on Hybrid Systems : Computation and Control |

Number of pages | 10 |

Publisher | Association for Computing Machinery |

Publication date | 11. Apr 2016 |

Pages | 257-266 |

ISBN (Electronic) | 9781450339551 |

DOIs | |

Publication status | Published - 11. Apr 2016 |

Externally published | Yes |

Event | 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016 - Vienna, Austria Duration: 12. Apr 2016 → 14. Apr 2016 |

### Conference

Conference | 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016 |
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Country/Territory | Austria |

City | Vienna |

Period | 12/04/2016 → 14/04/2016 |

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

## Keywords

- Hybrid Systems
- Optimisation
- Piecewisedeterministic Markov processes
- Sum of Squares
- Verification