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

  • Michèle Pelletier
Conference paper
First Online:
Part of the Lecture Notes in Control and Information Sciences book series (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.

Keywords

Exceptional Divisor Singular System Singular Control Adjoint Vector Geometric Singular Perturbation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Michèle Pelletier
    • 1
  1. 1.Laboratoire de TopologieUniversité de BourgogneDijon CedexFrance

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