## Abstract

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein distance. For this class of systems we derive control synthesis algorithms that are robust against all these distributions and maximize the probability of satisfying a reach-avoid specification, defined as the probability of reaching a goal region while being safe. The framework we present first learns an abstraction of a switched stochastic system as a robust Markov decision process (robust MDP) by accounting for both the stochasticity of the system and the uncertainty in the noise distribution. Then, it synthesizes a strategy on the resulting robust MDP that maximizes the probability of satisfying the property and is robust to all uncertainty in the system. This strategy is then refined into a switching strategy for the original stochastic system. By exploiting tools from optimal transport and stochastic programming, we show that synthesizing such a strategy reduces to solving a set of linear programs, thus guaranteeing efficiency. We experimentally validate the efficacy of our framework on various case studies, including both linear and non-linear switched stochastic systems. Our results represent the first formal approach for control synthesis of stochastic systems with uncertain noise distribution.

Original language | English |
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Title of host publication | Proceedings of the 26th ACM International Conference on Hybrid Systems, HSCC 2023 |

Subtitle of host publication | Computation and Control, Part of CPS-IoT Week |

Publisher | Association for Computing Machinery (ACM) |

Number of pages | 10 |

ISBN (Electronic) | 979-8-4007-0033-0 |

DOIs | |

Publication status | Published - 2023 |

Event | 26th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2023, Part of CPS-IoT Week 2023 - San Antonio, United States Duration: 10 May 2023 → 12 May 2023 |

### Conference

Conference | 26th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2023, Part of CPS-IoT Week 2023 |
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Country/Territory | United States |

City | San Antonio |

Period | 10/05/23 → 12/05/23 |

## Keywords

- Formal synthesis
- Safe autonomy
- Switched stochastic systems
- Uncertain Markov decision processes
- Wasserstein distance