Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions
Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions
复制标题
从时间最优控制角度看某些幂零分布的亚芬斯勒结构
DOI：
10.1007/s10883-016-9341-8
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Sigalotti
中科院分区：
文献类型：
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作者：
D. Barilari;U. Boscain;E. Donne;M. Sigalotti
在本文中，我们研究了次芬斯勒几何作为一个时间最优控制问题。特别是，我们认为非光滑和非严格凸的子Finsler结构与海森堡，Grushin和Martinet分布。受几何群论中问题的启发，我们刻画了极值曲线，讨论了它们的最优性，并计算了度量球面，证明了它们的欧几里得可求正性。
In this paper, we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability.