Singular Velocities of Even-Rank Affine Distributions

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• 作者：Marek Rupniewski (1)
  
  1. Faculty of Electronics and Information Technology ; Institute of Electronic Systems ; Warsaw University of Technology ; Nowowiejska 15/19 ; 00-665 ; Warsaw ; Poland
  
• 关键词：Affine distributions ; Singular extremals ; Singular curves ; 93B99 ; (55R10 ; 53B99)
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：21
• 期：2
• 页码：193-210
• 全文大小：403 KB
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  19. Rupniewski MW. Geometry of even rank affine distributions and their singular curves, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences. in Polish; 2008.
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

Singular curves, which are projections of singular extremals, play a special role in control theory and the theory of distributions. In this paper, we show that singular velocities, tangent to singular curves, determine affine distributions that are simultaneously of an even-rank and co-rank 2. If D is such a distribution, then its singular velocities span a distribution C D (of a rank two times smaller than that of D) that, together with its Lie square, forms the initial distribution, i.e., \(D={C^{D}}+\left [{C^{D}},{C^{D}}\right ]\) . We also provide canonical constructions of vector fields that are C D generators, canonical differential forms that are D cogenerators, and some functional invariants related to distribution of the considered type.