Model reduction through an Hankel problem and finite state machines
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology
2005
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/28724 |
| _version_ | 1811080686786838528 |
|---|---|
| author | Jameson, Neal Ward, 1978- |
| author2 | Alex Megretski. |
| author_facet | Alex Megretski. Jameson, Neal Ward, 1978- |
| author_sort | Jameson, Neal Ward, 1978- |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004. |
| first_indexed | 2024-09-23T11:34:52Z |
| format | Thesis |
| id | mit-1721.1/28724 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:34:52Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/287242019-04-11T03:32:45Z Model reduction through an Hankel problem and finite state machines Jameson, Neal Ward, 1978- Alex Megretski. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004. Includes bibliographical references (p. 30). (cont.) computation required to produce the approximation is O((n2Ì)/[epsilon]) where [epsilon] is the desired â[omega] error and n is the original system order. The problem of linear time invariant model reduction seeks to transform a given model into a model that has fidelity to the original but allows for easier completion of desired tasks such as controller design and simulation. Hankel-norm approximation consistently performs very well in terms of H[omega] error and provides lower bounds on how well any model can approximate the given model; however, it requires substantial and sometimes prohibitive computation to produce the reduced system and calculate the lower bounds. Here we present a Hankel like approximation problem that allows easier computation of lower bounds. It is shown that the lower bounds produced by the new method do a reasonable job of approximating the lower bounds produced by Hankel-norm approximation. On the negative side, It is also shown that, for the new Hankel problem, there can be no theorem analogous to the major theorem of Hankel-norm approximation that actually produces a reduced model. For nonlinear model reduction, model order does not always predict how difficult it is to perform desired tasks, so we introduce the idea of using finite state machines to approximate models. Lower state count for a finite machine indicates lower computational time to perform many tasks. First, we show, through finite state machine approximation of (1/s+1), that finite state machines are feasible as approximations. That is to say that the amount of states required to approximate a system does not blow up as desired fidelity is increased. We then show that for a given class of linear time invariant models we can set a desired â[omega] error and then find the finite state machine with the minimal number of states that achieves the desired error level. Moreover, the by Neal Ward Jameson, III. S.M. 2005-09-27T17:59:40Z 2005-09-27T17:59:40Z 2004 2004 Thesis http://hdl.handle.net/1721.1/28724 59554338 en_US 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 30 p. 950515 bytes 951246 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Jameson, Neal Ward, 1978- Model reduction through an Hankel problem and finite state machines |
| title | Model reduction through an Hankel problem and finite state machines |
| title_full | Model reduction through an Hankel problem and finite state machines |
| title_fullStr | Model reduction through an Hankel problem and finite state machines |
| title_full_unstemmed | Model reduction through an Hankel problem and finite state machines |
| title_short | Model reduction through an Hankel problem and finite state machines |
| title_sort | model reduction through an hankel problem and finite state machines |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/28724 |
| work_keys_str_mv | AT jamesonnealward1978 modelreductionthroughanhankelproblemandfinitestatemachines |