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

## TL;DR

This paper introduces a scalable method for safety verification of discrete-time affine systems using zonotope scaling to under-approximate invariant, viable, and discriminating kernels, demonstrated on toy and quadrotor models.

## Contribution

It presents a novel approach to construct invariant, viable, and discriminating sets via zonotope scaling and convex optimization, bridging a gap between reachability and viability analyses.

## Key findings

- Effective zonotope scaling method for set under-approximation.
- Demonstrated on toy examples and a 6D nonlinear quadrotor model.
- Provides scalable safety verification technique.

## Abstract

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.