Control and Integrability on SO (3)

Remsing, C.C. (2010) Control and Integrability on SO (3). Lecture Notes in Engineering and Computer Science, 2185 (1). pp. 1705-1710. ISSN 2078-0966

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Abstract

This paper considers control ane left- invariant systems evolving on matrix Lie groups. Such systems have signicant applications in a variety of elds. Any left-invariant optimal control problem (with quadratic cost) can be lifted, via the celebrated Maximum Principle, to a Hamiltonian system on the dual of the Lie algebra of the underlying state space G. The (minus) Lie-Poisson structure on the dual space g is used to describe the (normal) extremal curves. An interesting, and rather typical, single-input con- trol system on the rotation group SO (3) is investi- gated in some detail. The reduced Hamilton equa- tions associated with an extremal curve are derived in a simple and elegant manner. Finally, these equations are explicitly integrated by Jacobi elliptic functions.

Item Type:Article
Additional Information:Proceedings of the World Congress on Engineering 2010 Vol III WCE 2010, June 30 - July 2, 2010, London, U.K.
Uncontrolled Keywords:left-invariant control system, Pontryagin maximum principle, extremal curve, Lie-Poisson structure, elliptic function
Subjects:Q Science > QA Mathematics
Divisions:Faculty > Faculty of Science > Mathematics (Pure & Applied)
ID Code:1992
Deposited By: Mrs Eileen Shepherd
Deposited On:29 Jul 2011 13:22
Last Modified:06 Jan 2012 16:21
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