# Safe & Robust Reachability Analysis of Hybrid Systems

arXiv: https://arxiv.org/abs/1709.05658 · HTML: https://mlsanity.com/paper/1709.05658/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2017.

## Built on by (most cited first, 2 of 2)

- [Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics](https://mlsanity.com/paper/2212.00679/) (2022)
- [A Domain-Theoretic Framework for Robustness Analysis of Neural Networks](https://mlsanity.com/paper/2203.00295/) (2022)

## Abstract (arXiv)

Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability - namely, the reflexive and transitive closure of a transition relation - can be unsafe, ie, it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust wrt small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation.