On the internal stability of diffusively coupled multi-agent systems and the dangers of cancel culture
We study internal stability in the context of diffusively-coupled control architectures, common in multi-agent systems (i.e. the celebrated consensus protocol), for linear time-invariant agents. We derive a condition under which the system cannot be stabilized by any controller from that class. In t...
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Published in | Automatica (Oxford) Vol. 155; p. 111158 |
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Format | Journal Article |
Language | English |
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01.09.2023
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Abstract | We study internal stability in the context of diffusively-coupled control architectures, common in multi-agent systems (i.e. the celebrated consensus protocol), for linear time-invariant agents. We derive a condition under which the system cannot be stabilized by any controller from that class. In the finite-dimensional case the condition states that diffusive controllers cannot stabilize agents that share common unstable dynamics, directions included. This class always contains the group of homogeneous unstable agents, like integrators. We argue that the underlying reason is intrinsic cancellations of unstable agent dynamics by such controllers, even static ones, where directional properties play a key role. The intrinsic lack of internal stability explains the notorious behavior of some distributed control protocols when affected by measurement noise or exogenous disturbances. |
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AbstractList | We study internal stability in the context of diffusively-coupled control architectures, common in multi-agent systems (i.e. the celebrated consensus protocol), for linear time-invariant agents. We derive a condition under which the system cannot be stabilized by any controller from that class. In the finite-dimensional case the condition states that diffusive controllers cannot stabilize agents that share common unstable dynamics, directions included. This class always contains the group of homogeneous unstable agents, like integrators. We argue that the underlying reason is intrinsic cancellations of unstable agent dynamics by such controllers, even static ones, where directional properties play a key role. The intrinsic lack of internal stability explains the notorious behavior of some distributed control protocols when affected by measurement noise or exogenous disturbances. |
ArticleNumber | 111158 |
Author | Barkai, Gal Mirkin, Leonid Zelazo, Daniel |
Author_xml | – sequence: 1 givenname: Gal surname: Barkai fullname: Barkai, Gal email: galbarkai@campus.technion.ac.il organization: Faculty of Mechanical Engineering, Technion—IIT, Haifa 3200003, Israel – sequence: 2 givenname: Leonid surname: Mirkin fullname: Mirkin, Leonid email: mirkin@technion.ac.il organization: Faculty of Mechanical Engineering, Technion—IIT, Haifa 3200003, Israel – sequence: 3 givenname: Daniel surname: Zelazo fullname: Zelazo, Daniel email: dzelazo@technion.ac.il organization: Faculty of Aerospace Engineering, Technion—IIT, Haifa 3200003, Israel |
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Cites_doi | 10.1109/LCSYS.2017.2706948 10.1016/j.sysconle.2003.09.014 10.1007/s11424-018-7265-y 10.1016/j.automatica.2011.01.081 10.1080/00207178808906225 10.1090/S0002-9947-1968-0222701-7 10.1109/ACC.2012.6314791 10.1109/TIE.2015.2442218 10.1007/BF01211620 10.1109/TAC.2007.902733 10.2514/1.6165 10.1109/TAC.2010.2085312 10.1109/9.35819 10.1109/TSP.2009.2014812 10.1109/TAC.1981.1102770 10.1109/JSAC.2008.080507 10.1016/j.automatica.2014.10.081 10.1109/TAC.2010.2056730 10.1109/JPROC.2006.887293 |
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Title | On the internal stability of diffusively coupled multi-agent systems and the dangers of cancel culture |
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