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Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case

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Nonlinear control in the year 2000 volume 2

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 259))

Abstract

We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.

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Authors and Affiliations

  1. Laboratoire de Topologie, Université de Bourgogne, 9, avenue Alain Savary — BP 47870, 21078, Dijon Cedex, France

    Michèle Pelletier

Authors
  1. Michèle Pelletier
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Editor information

Alberto Isidori Françoise Lamnabhi-Lagarrigue Witold Respondek

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© 2001 Springer-Verlag London Limited

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Pelletier, M. (2001). Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110302

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  • DOI: https://doi.org/10.1007/BFb0110302

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-364-5

  • Online ISBN: 978-1-84628-569-1

  • eBook Packages: Springer Book Archive

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