通过 Zonotope Scaling 实现不变、可行与判别核欠逼近
Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling
AI总结：
本文针对具有对抗输入的离散时间仿射动态系统，通过缩放中心-生成器形式的 zonotopes 并利用凸优化求解缩放因子，构造了欠逼近不变核、可行核和判别核的集合，实现了可扩展的安全验证。
摘要：
使用参数化集合表示，通过可达性和可行性分析已经证明了对连续状态动态系统的可扩展安全验证；然而，对于此类参数化表示，这两种分析在实践中不可互换。本文考虑具有对抗输入的离散时间仿射动态系统的可行性分析。给定一组状态和输入约束，并以最佳和/或最坏情况处理输入，我们构造了不变、可行和判别集合，这些集合必须分别欠逼近不变核、可行核和判别核。这些集合通过缩放以中心-生成器形式表示的 zonotopes 来构造。缩放因子通过高效的凸优化求解。结果在两个玩具示例和一个四旋翼的六维非线性纵向模型上进行了演示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
