Abstract: We study in optimal control the important relation between invariance
of the problem under a family of transformations, and the existence
of preserved quantities along the Pontryagin extremals. Several extensions of
Noether's theorem are given, in the sense which enlarges the scope of its application.
The dissertation looks at extending the second Noether's theorem
to optimal control problems which are invariant under symmetry depending
upon k arbitrary functions of the independent variable and their derivatives
up to some order m. Furthermore, we look at the Conservation Laws, i.e.
conserved quantities along Euler-Lagrange extremals, which are obtained on
the basis of Noether's theorem.
And finally we obtain a generalization of Noether's theorem for optimal control
problems. The generalization involves a one-parameter family of smooth
maps which may depend also on the control and a Lagrangian which is invariant
up to an addition of an exact differential. / (M.Sc.) North-West University, Mafikeng Campus, 2005
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/11230 |
| Date | January 2005 |
| Creators | Tau, Baetsane Aaron |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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