Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11187
Title: Cubic polynomials and optimal control on compact Lie groups
Authors: Abrunheiro, L. 
Camarinha, M. 
Clemente-Gallardo, J. 
Keywords: Optimal control; Symplectic geometry; Riemannian geometry; Lie groups
Issue Date: 2009
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 09-05 (2009)
Abstract: This paper analyzes the Riemannian cubic polynomials’s problem from a Hamiltonian point of view. The description of the problem on compact Lie groups is particulary explored. The state space of the second order optimal control problem considered is the tangent bundle of the Lie group which also has a group structure. The dynamics of the problem is described by a presymplectic formalism associated with the canonical symplectic form on the cotangent bundle of the tangent bundle. Using these control geometrical tools, the equivalence between the Hamiltonian approach developed here and the known variational one is verified. Moreover, the equivalence allows us to deduce two invariants along the cubic polynomials which are in involution.
URI: http://hdl.handle.net/10316/11187
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

Files in This Item:
File Description SizeFormat
Cubic polynomials and optimal control on compact Lie groups.pdf203.29 kBAdobe PDFView/Open
Show full item record

Page view(s)

215
checked on Aug 18, 2022

Download(s) 50

273
checked on Aug 18, 2022

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.