- Title
- Contributions to the study of a class of optimal control problems on the matrix lie group SO(3)
- Creator
- Rodgerson, Joanne Kelly
- Subject
- Matrix groups
- Subject
- Lie groups
- Subject
- Maximum principles (Mathematics)
- Subject
- Elliptic functions
- Subject
- Extremal problems (Mathematics)
- Date Issued
- 2009
- Date
- 2009
- Date
- 2013-07-12
- Type
- Thesis
- Type
- Masters
- Type
- MSc
- Identifier
- vital:5421
- Identifier
- http://hdl.handle.net/10962/d1007199
- Identifier
- Matrix groups
- Identifier
- Lie groups
- Identifier
- Maximum principles (Mathematics)
- Identifier
- Elliptic functions
- Identifier
- Extremal problems (Mathematics)
- Description
- The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states.
- Description
- KMBT_363
- Description
- Adobe Acrobat 9.54 Paper Capture Plug-in
- Format
- 172 p.
- Format
- Publisher
- Rhodes University
- Publisher
- Faculty of Science, Mathematics
- Language
- English
- Rights
- Rodgerson, Joanne Kelly
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