Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

James Biggs, William Holderbaum

Research output: Contribution to conferencePaper

46 Downloads (Pure)

Abstract

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).
Original languageEnglish
Publication statusPublished - 2008
Event5th Wismar Symposium on Automatic Control, AUTSYM'08 - Wismar, Germany
Duration: 18 Sep 200819 Sep 2008

Conference

Conference5th Wismar Symposium on Automatic Control, AUTSYM'08
CityWismar, Germany
Period18/09/0819/09/08

Keywords

  • Hamiltonian systems
  • Lie groups
  • attitude control
  • spacecraft

Fingerprint Dive into the research topics of 'Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft'. Together they form a unique fingerprint.

Cite this