A Summary of Recent Progress on Efficient Parametric Approximations of Viability and Discriminating Kernels
A Summary of Recent Progress on Efficient Parametric Approximations of Viability and Discriminating Kernels
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生存能力的有效参数逼近和判别核的最新进展总结
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发表时间：
2015
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通讯作者：
Ian M. Mitchell
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作者：
Ian M. Mitchell
生存能力和判别内核是强大的结构，通过模型检查分析系统的安全性，但直到最近唯一可用的计算算法是非参数网格为基础的方法，虽然准确，指数缩放与系统的状态空间的维度。相比之下，几个多项式复杂度的可达性算法已经开发出使用各种参数集表示。在最近的一系列论文中，其中两个参数的方法-基于椭球和支持向量-已被改编为近似的可行性和判别内核的离散，连续和采样数据模型的时间。本文简要总结了这些算法，并比较它们的关键功能彼此之间，并与一个有代表性的非参数方法。
Viability and discriminating kernels are powerful constructs for analyzing system safety through model checking, but until recently the only computational algorithms available were nonparametric gridbased approaches which, although accurate, scaled exponentially with the dimension of the system’s state space. In contrast, several polynomial complexity reachability algorithms have been developed using various parametric set representations. In a recent series of papers, two of these parametric approaches—based on ellipsoids and support vectors—have been adapted to approximate viability and discriminating kernels in the discrete, continuous and sampled data models of time. This paper briefly summarizes these algorithms and compares their key features with one another and with a representative nonparametric approach.