A New Condition for Convergence in Continuous-Time 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)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73572 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1811083706509557760 |
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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 present a result guaranteeing the convergence of every cut-balanced system, and giving a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. This condition is also necessary up to a zero-measure subset of the initial conditions. Using the fact that our convergence requires no additional condition, we show that it also applies to systems where the agent connectivity and interactions are random, or endogenous, that is, determined by the agent values. We also derive corresponding results for discrete-time systems. |
| first_indexed | 2024-09-23T12:37:49Z |
| format | Article |
| id | mit-1721.1/73572 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:37:49Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/735722022-09-28T09:04:57Z A New Condition for Convergence in Continuous-Time 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 Hendrickx, Julien 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 present a result guaranteeing the convergence of every cut-balanced system, and giving a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. This condition is also necessary up to a zero-measure subset of the initial conditions. Using the fact that our convergence requires no additional condition, we show that it also applies to systems where the agent connectivity and interactions are random, or endogenous, that is, determined by the agent values. We also derive corresponding results for discrete-time systems. National Science Foundation (U.S.) (Grant ECCS-0701623) Belgian American Educational Foundation, inc. (Fellowship) Belgian National Foundation for Scientific Research (Fellowship) 2012-10-03T17:57:28Z 2012-10-03T17:57:28Z 2011-12 2011-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-61284-799-3 978-1-61284-800-6 0743-1546 http://hdl.handle.net/1721.1/73572 Hendrickx, Julien M., and John N. Tsitsiklis. “A New Condition for Convergence in Continuous-time Consensus Seeking Systems.” 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011. 5070–5075. https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/10.1109/CDC.2011.6160231 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) Other University Web Domain |
| spellingShingle | Hendrickx, Julien Tsitsiklis, John N. A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title | A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title_full | A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title_fullStr | A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title_full_unstemmed | A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title_short | A New Condition for Convergence in Continuous-Time Consensus Seeking Systems |
| title_sort | new condition for convergence in continuous time consensus seeking systems |
| url | http://hdl.handle.net/1721.1/73572 https://orcid.org/0000-0003-2658-8239 |
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