Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems
We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetri...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90991 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1811096782889811968 |
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| author | Hendrickx, Julien Tsitsiklis, John N. |
| 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 Hendrickx, Julien Tsitsiklis, John N. |
| author_sort | Hendrickx, Julien |
| collection | MIT |
| description | We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases. We prove that such systems always converge. We give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. Conversely, we show that if our condition is not satisfied, then these limits are generically different. These results allow treating systems where the agent interactions are a priori unknown, being for example random or determined endogenously by the agent values. |
| first_indexed | 2024-09-23T16:48:58Z |
| format | Article |
| id | mit-1721.1/90991 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:48:58Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/909912022-09-29T21:41:33Z Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems Hendrickx, Julien Tsitsiklis, John N. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Tsitsiklis, John N. We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases. We prove that such systems always converge. We give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. Conversely, we show that if our condition is not satisfied, then these limits are generically different. These results allow treating systems where the agent interactions are a priori unknown, being for example random or determined endogenously by the agent values. National Science Foundation (U.S.) (Grant ECCS-0701623) 2014-10-20T16:53:27Z 2014-10-20T16:53:27Z 2012-12 2012-05 Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 http://hdl.handle.net/1721.1/90991 Hendrickx, Julien M., and John N. Tsitsiklis. “Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems.” IEEE Trans. Automat. Contr. 58, no. 1 (January 2013): 214–218. https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/10.1109/tac.2012.2203214 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Hendrickx, Julien Tsitsiklis, John N. Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title | Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title_full | Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title_fullStr | Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title_full_unstemmed | Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title_short | Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems |
| title_sort | convergence of type symmetric and cut balanced consensus seeking systems |
| url | http://hdl.handle.net/1721.1/90991 https://orcid.org/0000-0003-2658-8239 |
| work_keys_str_mv | AT hendrickxjulien convergenceoftypesymmetricandcutbalancedconsensusseekingsystems AT tsitsiklisjohnn convergenceoftypesymmetricandcutbalancedconsensusseekingsystems |