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. / KMBT_363 / Adobe Acrobat 9.54 Paper Capture Plug-in
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5421 |
| Date | 12 July 2013 |
| Creators | Rodgerson, Joanne Kelly |
| Publisher | Rhodes University, Faculty of Science, Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Masters, MSc |
| Format | 172 p., pdf |
| Rights | Rodgerson, Joanne Kelly |
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