Biggs, James D. 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, Seville, Spain.
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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.
|Item type:||Conference or Workshop Item (Paper)|
|Keywords:||geometry, optimal control problems, six dimensional lie groups, control systems, Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Physics, Aerospace Engineering, Control and Systems Engineering, Space and Planetary Science|
|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:||15 Apr 2015 14:58|
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