### Abstract

Language | English |
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Pages | 1427-1432 |

Number of pages | 6 |

Publication status | Published - 2006 |

Event | 44th IEEE Conference on Decision and Control/European Control Conference - Seville, Spain Duration: 12 Dec 2005 → … |

### Conference

Conference | 44th IEEE Conference on Decision and Control/European Control Conference |
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City | Seville, Spain |

Period | 12/12/05 → … |

### Fingerprint

### Keywords

- geometry
- optimal control problems
- six dimensional lie groups
- control systems

### Cite this

*The geometry of optimal control problems on some six dimensional lie groups*. 1427-1432. Paper presented at 44th IEEE Conference on Decision and Control/European Control Conference, Seville, Spain, .

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**The geometry of optimal control problems on some six dimensional lie groups.** / Biggs, James; Holderbaum, William.

Research output: Contribution to conference › Paper

TY - CONF

T1 - The geometry of optimal control problems on some six dimensional lie groups

AU - Biggs, James

AU - Holderbaum, William

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - geometry

KW - optimal control problems

KW - six dimensional lie groups

KW - control systems

M3 - Paper

SP - 1427

EP - 1432

ER -