Computing Distances between Reach Flowpipes
Computing Distances between Reach Flowpipes
复制标题
计算前移流量管之间的距离
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Vinayak S. Prabhu
中科院分区：
文献类型：
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作者：
R. Majumdar;Vinayak S. Prabhu
我们研究了在噪声和初始状态不确定性下两个混合动力系统之间的差异的量化。虽然这些系统的迹集是无限的，但可以使用计算可达集随时间演化的上界和下界的{reachpipes}来象征性地近似迹集。我们估计两个系统的轨迹之间的距离在reachpipes之间的距离。在两个单独的轨迹的情况下，Skorokhod距离已经被提出作为捕获值和定时失真的鲁棒且有效的距离概念。在本文中，我们扩展的Skorokhod距离的计算到达管道，并提供算法来计算两组轨迹之间的距离的上限和下限。我们的算法使用新的几何见解，用于计算随时间演变的两个多面体集之间的最坏情况和最佳情况的距离。
We investigate quantifying the difference between two hybrid dynamical systems under noise and initial-state uncertainty. While the set of traces for these systems is infinite, it is possible to symbolically approximate trace sets using emph{reachpipes} that compute upper and lower bounds on the evolution of the reachable sets with time. We estimate distances between corresponding sets of trajectories of two systems in terms of distances between the reachpipes. In case of two individual traces, the Skorokhod distance has been proposed as a robust and efficient notion of distance which captures both value and timing distortions. In this paper, we extend the computation of the Skorokhod distance to reachpipes, and provide algorithms to compute upper and lower bounds on the distance between two sets of traces. Our algorithms use new geometric insights that are used to compute the worst-case and best-case distances between two polyhedral sets evolving with time.