# Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling

arXiv: https://arxiv.org/abs/1901.01006 · HTML: https://mlsanity.com/paper/1901.01006/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2019.

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

- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Excluding the Irrelevant: Focusing Reinforcement Learning through Continuous Action Masking](https://mlsanity.com/paper/2406.03704/) (2024)
- [Data-Driven Reachability analysis and Support set Estimation with Christoffel Functions](https://mlsanity.com/paper/2112.09995/) (2021)

## Abstract (arXiv)

Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for such parametric representations. In this paper we consider viability analysis for discrete time affine dynamic systems with adversarial inputs. Given a set of state and input constraints, and treating the inputs in best-case and/or worst-case fashion, we construct invariant, viable and discriminating sets, which must therefore under-approximate the invariant, viable and discriminating kernels respectively. The sets are constructed by scaling zonotopes represented in center-generator form. The scale factors are found through efficient convex optimizations. The results are demonstrated on two toy examples and a six dimensional nonlinear longitudinal model of a quadrotor.