Contraction analysis of nonlinear systems
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/9793 |
| _version_ | 1826215237850759168 |
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| author | Lohmiller, Winfried Stefan, 1971- |
| author2 | Jean-Jacques E. Slotine. |
| author_facet | Jean-Jacques E. Slotine. Lohmiller, Winfried Stefan, 1971- |
| author_sort | Lohmiller, Winfried Stefan, 1971- |
| collection | MIT |
| description | Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999. |
| first_indexed | 2024-09-23T16:20:33Z |
| format | Thesis |
| id | mit-1721.1/9793 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:20:33Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/97932020-04-27T20:59:33Z Contraction analysis of nonlinear systems Lohmiller, Winfried Stefan, 1971- Jean-Jacques E. Slotine. Massachusetts Institute of Technology. Department of Mechanical Engineering Mechanical Engineering Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999. Includes bibliographical references (leaves 87-90). This thesis derives new results in nonlinear system analysis using methods inspired from fluid mechanics and differential geometry. Based on a differential analysis of convergence, these results may be viewed as generalizing the classical Krasovskii theorem, as well as linear eigenvalue analysis. A central feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual simplifications. We establish new combination properties of nonlinear dynamic systems and use them to derive simple controller and observer designs for mechanical systems such as aircraft, underwater vehicles, and robots. The method is also applied to chemical chain reactions and mixture processes. The relative simplicity of these designs stems from their effective exploitation of the systems' structural specificities. Next, we analyze and quantify the global stability properties of physical partial differential equations such as the heat equation, or the Schroedinger equation. Lyapunov exponents are not coordinate-invariant, and thus their exact physical meaning is somewhat questionable. As an alternative, we suggest an extension of linear eigenvalue analysis to nonlinear dynamic systems. Finally, the thesis derives new controller and observer designs for general nonlinear dynamic systems. In particular, an extension of feedback linearization is proposed when the corresponding integrability conditions are violated. by Winfried Stefan Lohmiller. Ph.D. 2005-08-19T20:13:05Z 2005-08-19T20:13:05Z 1999 1999 Thesis http://hdl.handle.net/1721.1/9793 42916380 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 90 leaves 5848748 bytes 5848504 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering Lohmiller, Winfried Stefan, 1971- Contraction analysis of nonlinear systems |
| title | Contraction analysis of nonlinear systems |
| title_full | Contraction analysis of nonlinear systems |
| title_fullStr | Contraction analysis of nonlinear systems |
| title_full_unstemmed | Contraction analysis of nonlinear systems |
| title_short | Contraction analysis of nonlinear systems |
| title_sort | contraction analysis of nonlinear systems |
| topic | Mechanical Engineering |
| url | http://hdl.handle.net/1721.1/9793 |
| work_keys_str_mv | AT lohmillerwinfriedstefan1971 contractionanalysisofnonlinearsystems |