A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation
In this paper, we revisit standard results for singularly perturbed systems on the infinite time interval by employing tools from nonlinear contraction theory. This allows us to determine explicit bounds both on the rate of convergence of trajectories to the slow manifold, and on the distance betwee...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2013
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| Online Access: | http://hdl.handle.net/1721.1/79864 https://orcid.org/0000-0001-6472-8576 https://orcid.org/0000-0002-7161-7812 |
| _version_ | 1826207575635394560 |
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| author | Del Vecchio, Domitilla Slotine, Jean-Jacques E. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Del Vecchio, Domitilla Slotine, Jean-Jacques E. |
| author_sort | Del Vecchio, Domitilla |
| collection | MIT |
| description | In this paper, we revisit standard results for singularly perturbed systems on the infinite time interval by employing tools from nonlinear contraction theory. This allows us to determine explicit bounds both on the rate of convergence of trajectories to the slow manifold, and on the distance between these trajectories and those of the reduced system. We illustrate the application of the proposed technique to the problem of retroactivity attenuation in biomolecular systems, that is, to the problem of attenuating the effects of output loading due to interconnection to downstream systems. By virtue of the explicit bounds, we can single out the key biochemical parameters to tune in order to enhance retroactivity attenuation. This provides design guidelines for synthetic biology devices that are robust to loading and can function as insulation devices just like insulating amplifiers work in electronics. |
| first_indexed | 2024-09-23T13:51:42Z |
| format | Article |
| id | mit-1721.1/79864 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:51:42Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/798642022-10-01T17:33:14Z A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation Del Vecchio, Domitilla Slotine, Jean-Jacques E. Massachusetts Institute of Technology. Department of Mechanical Engineering Del Vecchio, Domitilla Slotine, Jean-Jacques E. In this paper, we revisit standard results for singularly perturbed systems on the infinite time interval by employing tools from nonlinear contraction theory. This allows us to determine explicit bounds both on the rate of convergence of trajectories to the slow manifold, and on the distance between these trajectories and those of the reduced system. We illustrate the application of the proposed technique to the problem of retroactivity attenuation in biomolecular systems, that is, to the problem of attenuating the effects of output loading due to interconnection to downstream systems. By virtue of the explicit bounds, we can single out the key biochemical parameters to tune in order to enhance retroactivity attenuation. This provides design guidelines for synthetic biology devices that are robust to loading and can function as insulation devices just like insulating amplifiers work in electronics. National Science Foundation (U.S.). Division of Computing and Communication Foundations (NSF-CCF Grant 1058127) 2013-08-14T16:53:10Z 2013-08-14T16:53:10Z 2011-12 Article http://purl.org/eprint/type/JournalArticle 978-1-61284-799-3 978-1-61284-800-6 0743-1546 http://hdl.handle.net/1721.1/79864 Del Vecchio, Domitilla, and Jean-Jacques Slotine. “A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation.” IEEE, 2011. 5831–5836. https://orcid.org/0000-0001-6472-8576 https://orcid.org/0000-0002-7161-7812 en_US http://dx.doi.org/10.1109/CDC.2011.6160340 Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011 Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Del Vecchio, Domitilla Slotine, Jean-Jacques E. A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title | A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title_full | A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title_fullStr | A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title_full_unstemmed | A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title_short | A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation |
| title_sort | contraction theory approach to singularly perturbed systems with application to retroactivity attenuation |
| url | http://hdl.handle.net/1721.1/79864 https://orcid.org/0000-0001-6472-8576 https://orcid.org/0000-0002-7161-7812 |
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