- Title
- Left-invariant optimal control problems on the Heisenberg group and the associated Hamilton-Poisson systems: classification, stability and integration
- Creator
- Bartlett, Catherine Eve
- ThesisAdvisor
- Remsing, C.C.
- Subject
- Uncatalogued
- Date
- 2015-04-10
- Type
- Academic theses
- Type
- Master's theses
- Type
- text
- Identifier
- http://hdl.handle.net/10962/480312
- Identifier
- vital:78428
- Description
- This thesis examines the left-invariant control affine systems of full rank, evolving on the three-dimensional Heisenberg group H3. Such systems are classified under state space equivalence, detached feedback equivalence and strongly detached feedback equivalence; a complete list of equivalence representatives is obtained. The equivalence of cost-extended control systems corresponding to left-invariant optimal control problems on H3 with fixed terminal time, affine dynamics, and affine quadratic cost is also considered. To left-invariant optimal control problems on H3 with quadratic cost, one may, via the Pontryagin Maximum Principle, associate a quadratic Hamilton-Poisson system on the (minus) Lie-Poisson space h3. Homogeneous and inhomogeneous quadratic Hamilton-Poisson systems are investigated. These systems are classified up to an affine isomorphism. Furthermore, the stability nature of the equilibria of the systems are analysed and explicit expressions for all integral curves are determined.
- Description
- Thesis (MSc) -- Faculty of Science, Mathematics (Pure and Applied), 2015
- Format
- computer, online resource, application/pdf, 1 online resource (157 pages), pdf
- Publisher
- Rhodes University, Faculty of Science, Mathematics (Pure and Applied)
- Language
- English
- Rights
- Bartlett, Catherine Eve
- Rights
- Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-ShareAlike" License (http://creativecommons.org/licenses/by-nc-sa/2.0/)
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | BARTLETT-MSc-TR15-272_embargo 2 years extended to May 2018.pdf | 1002 KB | Adobe Acrobat PDF | View Details Download |