Remsing, C.C. (2010) Control and Integrability on SO (3). Lecture Notes in Engineering and Computer Science, 2185 (1). pp. 17051710. ISSN 20780966

Text
remsing_Control_Integrability.pdf 856Kb 
Official URL: http://www.iaeng.org/LNECS/
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 leftinvariant 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) LiePoisson structure on the dual space g is used to describe the (normal) extremal curves. An interesting, and rather typical, singleinput 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:  leftinvariant control system, Pontryagin maximum principle, extremal curve, LiePoisson 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 
23 fulltext download(s) in the past 12 months
More statistics...
Repository Staff Only: item control page