Mesh-Based Piecewise Affine Abstraction With Polytopic Partitions for Nonlinear Systems
Mesh-Based Piecewise Affine Abstraction With Polytopic Partitions for Nonlinear Systems
复制标题
非线性系统的基于网格的多面划分的分段仿射抽象
DOI：
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发表时间：
2021
影响因子：
3
通讯作者：
Sze Zheng Yong
中科院分区：
文献类型：
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作者：
Zeyuan Jin;Qiang Shen;Sze Zheng Yong
这封信考虑的问题分段仿射抽象与多面体分区的非线性系统，即，在包含所有可能轨迹的意义上，在多面体子域/分区上通过一对分段仿射函数对非线性动力学进行过逼近。具体来说，为了解决“边界效应”，可能会使过度近似不正确的多面体分区，我们提出了两个基于网格的仿射抽象方法的基础上扩展的分区，同时找到多面体分区和分区上的分段函数对。所提出的方法的有效性进行了比较，与现有的方法使用超矩形分区，并证明了计算抽象的群体动力学和应用它们的群体意图识别。
This letter considers the problem of piecewise affine abstraction with polytopic partitions of nonlinear systems, i.e., the over-approximation of nonlinear dynamics by a pair of piecewise affine functions over polytopic subdomains/partitions in the sense of the inclusion of all possible trajectories. Specifically, to tackle the “boundary effect” that may make the over-approximation incorrect for polytopic partitions, we propose two mesh-based affine abstraction approaches based on expanding the partitions to simultaneously find the polytopic partitions and the pair of piecewise functions over the partitions. The effectiveness of the proposed approaches are compared with existing methods using hyperrectangular partitions, and demonstrated by computing abstractions of swarm dynamics and applying them for swarm intent identification.