Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

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• 作者：Yasir Awais Butt ; Yuri L. Sachkov…
• 关键词：Sub ; Riemannian geometry ; Special hyperbolic group SH(2) ; Maxwell points ; Cut time ; Conjugate time ; Optimal synthesis
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：155-195
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control;
• 出版者：Springer US
• ISSN：1573-8698
• 卷排序：23

文摘

Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and obtain an explicit description of cut locus and optimal synthesis.