Computational analysis of real-time convex optimization for control systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000.
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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/1721.1/9174 |
| _version_ | 1826216257373863936 |
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| author | McGovern, Lawrence Kent |
| author2 | Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics McGovern, Lawrence Kent |
| author_sort | McGovern, Lawrence Kent |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000. |
| first_indexed | 2024-09-23T16:44:30Z |
| format | Thesis |
| id | mit-1721.1/9174 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:44:30Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/91742019-04-12T08:58:02Z Computational analysis of real-time convex optimization for control systems McGovern, Lawrence Kent Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics Aeronautics and Astronautics Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000. Includes bibliographical references (p. 177-189). Computational analysis is fundamental for certification of all real-time control software. Nevertheless, analysis of on-line optimization for control has received little attention to date. On-line software must pass rigorous standards in reliability, requiring that any embedded optimization algorithm possess predictable behavior and bounded run-time guarantees. This thesis examines the problem of certifying control systems which utilize real-time optimization. A general convex programming framework is used, to which primal-dual path-following algorithms are applied. The set of all optimization problem instances which may arise in an on-line procedure is characterized as a compact parametric set of convex programming problems. A method is given for checking the feasibility and well-posedness of this compact set of problems, providing certification that every problem instance has a solution and can be solved in finite time. The thesis then proposes several algorithm initialization methods, considering the fixed and time-varying constraint cases separately. Computational bounds are provided for both cases. In the event that the computational requirements cannot be met, several alternatives to on-line optimization are suggested. Of course, these alternatives must provide feasible solutions with minimal real-time computational overhead. Beyond this requirement, these methods approximate the optimal solution as well as possible. The methods explored include robust table look-up, functional approximation of the solution set, and ellipsoidal approximation of the constraint set. The final part of this thesis examines the coupled behavior of a receding horizon control scheme for constrained linear systems and real-time optimization. The driving requirement is to maintain closed-loop stability, feasibility and well-posedness of the optimal control problem, and bounded iterations for the optimization algorithm. A detailed analysis provides sufficient conditions for meeting these requirements. A realistic example of a small autonomous air vehicle is furnished, showing how a receding horizon control law using real-time optimization can be certified. by Lawrence Kent McGovern. Ph.D. 2005-08-22T23:17:26Z 2005-08-22T23:17:26Z 2000 2000 Thesis http://hdl.handle.net/1721.1/9174 45448776 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://theses.mit.edu/Dienst/UI/2.0/Describe/0018.mit.theses%2f2000-48?abstract= http://dspace.mit.edu/handle/1721.1/7582 189 p. 17441644 bytes 17441396 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Aeronautics and Astronautics McGovern, Lawrence Kent Computational analysis of real-time convex optimization for control systems |
| title | Computational analysis of real-time convex optimization for control systems |
| title_full | Computational analysis of real-time convex optimization for control systems |
| title_fullStr | Computational analysis of real-time convex optimization for control systems |
| title_full_unstemmed | Computational analysis of real-time convex optimization for control systems |
| title_short | Computational analysis of real-time convex optimization for control systems |
| title_sort | computational analysis of real time convex optimization for control systems |
| topic | Aeronautics and Astronautics |
| url | http://hdl.handle.net/1721.1/9174 |
| work_keys_str_mv | AT mcgovernlawrencekent computationalanalysisofrealtimeconvexoptimizationforcontrolsystems |