The geometry of optimal control problems on some six dimensional lie groups

Biggs, James and Holderbaum, William (2006) The geometry of optimal control problems on some six dimensional lie groups. In: 44th IEEE Conference on Decision and Control/European Control Conference, 2005-12-12.

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Abstract

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E3 , the spheres S3 and the hyperboloids H3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

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• Item metadata

  Item type:	Conference or Workshop Item(Paper)
  ID code:	8059
  Dates:	Date Event 2006 Published
  Subjects:	Technology > Mechanical engineering and machinery Technology > Motor vehicles. Aeronautics. Astronautics Science > Physics
  Department:	Faculty of Engineering > Mechanical and Aerospace Engineering
  Depositing user:	Ms Katrina May
  Date deposited:	05 Jun 2009 12:41
  Last modified:	12 Dec 2024 16:10
  URI:	https://strathprints.strath.ac.uk/id/eprint/8059