Classical and Strong Convexity of Sublevel Sets and Application to Attainable Sets of Nonlinear Systems
Classical and Strong Convexity of Sublevel Sets and Application to Attainable Sets of Nonlinear Systems
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DOI：
10.1137/130945983
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
Alexander Weber;G. Reissig
中科院分区：
文献类型：
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作者：
Alexander Weber;G. Reissig
给出了由多个实值$C^{1，1}$-映射定义的子水平集分别为凸和强凸的充要条件。证明了强凸集的一个新的局部二次支撑刻画。利用强凸性的结果，得到了连续时间非线性系统可达集是强凸的充分条件。这些条件的应用是一种新的方法来过近似可达集时，强凸性。
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.