# Lagrangian Reachabililty

arXiv: https://arxiv.org/abs/1705.05927 · HTML: https://mlsanity.com/paper/1705.05927/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2017.

## Built on by (most cited first, 3 of 3)

- [GoTube: Scalable Stochastic Verification of Continuous-Depth Models](https://mlsanity.com/paper/2107.08467/) (2021)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Robustness Analysis of Continuous-Depth Models with Lagrangian Techniques](https://mlsanity.com/paper/2308.12192/) (2023)

## Abstract (arXiv)

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.