An optimal controller architecture for poset-causal systems
We propose a novel and natural architecture for decentralized control, that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the Möbius transform of the poset, and enjoys simple and appealing separation proper...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/72482 https://orcid.org/0000-0003-1132-8477 |
| _version_ | 1826215015957397504 |
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| author | Shah, Parikshit Parrilo, Pablo A. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Shah, Parikshit Parrilo, Pablo A. |
| author_sort | Shah, Parikshit |
| collection | MIT |
| description | We propose a novel and natural architecture for decentralized control, that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the Möbius transform of the poset, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Möbius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on ℌ2-optimal decentralized control for arbitrary posets, we prove that the ℌ2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture. |
| first_indexed | 2024-09-23T16:15:31Z |
| format | Article |
| id | mit-1721.1/72482 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:15:31Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/724822022-10-02T07:18:03Z An optimal controller architecture for poset-causal systems Shah, Parikshit Parrilo, Pablo A. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Parrilo, Pablo A. Shah, Parikshit Parrilo, Pablo A. We propose a novel and natural architecture for decentralized control, that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the Möbius transform of the poset, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Möbius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on ℌ2-optimal decentralized control for arbitrary posets, we prove that the ℌ2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture. 2012-08-30T18:35:57Z 2012-08-30T18:35:57Z 2012-03 2011-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-61284-799-3 978-1-61284-800-6 http://hdl.handle.net/1721.1/72482 Shah, Parikshit, and Pablo A. Parrilo. “An Optimal Controller Architecture for Poset-causal Systems.” 50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC). 5522–5528. https://orcid.org/0000-0003-1132-8477 en_US http://dx.doi.org/10.1109/CDC.2011.6160816 50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC) 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 | Shah, Parikshit Parrilo, Pablo A. An optimal controller architecture for poset-causal systems |
| title | An optimal controller architecture for poset-causal systems |
| title_full | An optimal controller architecture for poset-causal systems |
| title_fullStr | An optimal controller architecture for poset-causal systems |
| title_full_unstemmed | An optimal controller architecture for poset-causal systems |
| title_short | An optimal controller architecture for poset-causal systems |
| title_sort | optimal controller architecture for poset causal systems |
| url | http://hdl.handle.net/1721.1/72482 https://orcid.org/0000-0003-1132-8477 |
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