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.

中文翻译：

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非线性系统的基于网格的多面划分的分段仿射抽象


这封信考虑了非线性系统多面划分的分段仿射抽象问题，即在包含所有可能轨迹的意义上，多面子域/划分上的一对分段仿射函数对非线性动力学的过度逼近。具体来说，为了解决可能使多面分区的过度近似不正确的“边界效应”，我们提出了两种基于网格的仿射抽象方法，基于扩展分区以同时找到多面分区和分区上的一对分段函数。将所提出的方法的有效性与使用超矩形分区的现有方法进行比较，并通过计算群体动力学的抽象并将其应用于群体意图识别来证明。