Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling
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.
Cite
@article{arxiv.1901.01006,
title = {Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling},
author = {Ian M. Mitchell and Jacob Budzis and Andriy Bolyachevets},
journal= {arXiv preprint arXiv:1901.01006},
year = {2024}
}