### Abstract

Original language | English |
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Publication status | Published - 2008 |

Event | 5th Wismar Symposium on Automatic Control, AUTSYM'08 - Wismar, Germany Duration: 18 Sep 2008 → 19 Sep 2008 |

### Conference

Conference | 5th Wismar Symposium on Automatic Control, AUTSYM'08 |
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City | Wismar, Germany |

Period | 18/09/08 → 19/09/08 |

### Fingerprint

### Keywords

- Hamiltonian systems
- Lie groups
- attitude control
- spacecraft

### Cite this

*Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft*. Paper presented at 5th Wismar Symposium on Automatic Control, AUTSYM'08, Wismar, Germany, .

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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, James; Holderbaum, William.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2)

T2 - an application to the attitude control of a spacecraft

AU - Biggs, James

AU - Holderbaum, William

PY - 2008

Y1 - 2008

N2 - 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).

AB - 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).

KW - Hamiltonian systems

KW - Lie groups

KW - attitude control

KW - spacecraft

M3 - Paper

ER -