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

Biggs, J.D. and Holderbaum, William (2008) Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft. In: 5th Wismar Symposium on Automatic Control, AUTSYM'08, 2008-09-18 - 2008-09-19, Wismar, Germany.

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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).

Item type: Conference or Workshop Item (Paper)
ID code: 8100
Keywords: Hamiltonian systems, Lie groups, attitude control, spacecraft, Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Aerospace Engineering, Control and Systems Engineering, Space and Planetary Science
Subjects: Technology > Mechanical engineering and machinery
Technology > Motor vehicles. Aeronautics. Astronautics
Department: Faculty of Engineering > Mechanical and Aerospace Engineering
Depositing user: Ms Katrina May
Date Deposited: 10 Jun 2009 12:28
Last modified: 21 Jul 2015 12:45
URI: http://strathprints.strath.ac.uk/id/eprint/8100

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