### Abstract

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution-flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.

Original language | English |
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Title of host publication | Computer Aided Verification - 29th International Conference, CAV 2017, Proceedings |

Editors | Viktor Kuncak, Rupak Majumdar |

Publisher | Springer-Verlag |

Pages | 379-400 |

Number of pages | 22 |

ISBN (Print) | 9783319633862 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 29th International Conference on Computer Aided Verification, CAV 2017 - Heidelberg, Germany Duration: Jul 24 2017 → Jul 28 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10426 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 29th International Conference on Computer Aided Verification, CAV 2017 |
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Country | Germany |

City | Heidelberg |

Period | 07/24/17 → 07/28/17 |

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### Cite this

*Computer Aided Verification - 29th International Conference, CAV 2017, Proceedings*(pp. 379-400). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10426 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-63387-9_19