# Lazy Abstraction-Based Control for Safety Specifications

arXiv: https://arxiv.org/abs/1804.02666 · HTML: https://mlsanity.com/paper/1804.02666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Efficient Shield Synthesis via State-Space Transformation](https://mlsanity.com/paper/2407.19911/) (2024)

## Abstract (arXiv)

We present a lazy version of multi-layered abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against safety specifications. State-of-the-art multi-layered ABCS uses pre-computed finite-state abstractions of different coarseness. Our new algorithm improves this technique by computing transitions on-the-fly, and only when a particular region of the state space needs to be explored by the controller synthesis algorithm for a specific coarseness. Additionally, our algorithm improves upon existing techniques by using coarser cells on a larger subset of the state space, which leads to significant computational savings.