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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| Main Authors | , , |
| 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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relative sensing and switched information publication-title: Journal of Guidance, Control, and Dynamics doi: 10.2514/1.6165 contributor: fullname: Smith – year: 2005 ident: 10.1016/j.automatica.2023.111158_b21 contributor: fullname: Skogestad – year: 2010 ident: 10.1016/j.automatica.2023.111158_b13 contributor: fullname: Mesbahi – volume: 56 start-page: 971 issue: 5 year: 2011 ident: 10.1016/j.automatica.2023.111158_b30 article-title: Graph-theoretic analysis and synthesis of relative sensing networks publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2010.2085312 contributor: fullname: Zelazo – volume: 34 start-page: 1005 issue: 9 year: 1989 ident: 10.1016/j.automatica.2023.111158_b22 article-title: On stabilization and the existence of coprime factorizations publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.35819 contributor: fullname: Smith – volume: 57 start-page: 2000 issue: 5 year: 2009 ident: 10.1016/j.automatica.2023.111158_b12 article-title: Distributed sensor localization in random environments using minimal number of anchor nodes publication-title: IEEE Transactions on Signal Processing doi: 10.1109/TSP.2009.2014812 contributor: fullname: Khan – volume: 26 start-page: 1133 issue: 5 year: 1981 ident: 10.1016/j.automatica.2023.111158_b1 article-title: Time-varying feedback laws for decentralized control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.1981.1102770 contributor: fullname: Anderson – volume: 26 start-page: 650 issue: 4 year: 2008 ident: 10.1016/j.automatica.2023.111158_b24 article-title: Distributed function calculation and consensus using linear iterative strategies publication-title: IEEE Journal on Selected Areas in Communications doi: 10.1109/JSAC.2008.080507 contributor: fullname: Sundaram – year: 2020 ident: 10.1016/j.automatica.2023.111158_b7 contributor: fullname: Davison – year: 2022 ident: 10.1016/j.automatica.2023.111158_b4 contributor: fullname: Bullo – year: 1996 ident: 10.1016/j.automatica.2023.111158_b31 contributor: fullname: Zhou – volume: 51 start-page: 210 year: 2015 ident: 10.1016/j.automatica.2023.111158_b5 article-title: Dynamic coupling design for nonlinear output agreement and time-varying flow control publication-title: Automatica doi: 10.1016/j.automatica.2014.10.081 contributor: fullname: Bürger – year: 2001 ident: 10.1016/j.automatica.2023.111158_b11 contributor: fullname: Godsil – year: 2019 ident: 10.1016/j.automatica.2023.111158_b14 contributor: fullname: Mirkin – volume: 56 start-page: 544 issue: 3 year: 2011 ident: 10.1016/j.automatica.2023.111158_b29 article-title: Edge agreement: Graph-theoretic performance bounds and passivity analysis publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2010.2056730 contributor: fullname: Zelazo – year: 1987 ident: 10.1016/j.automatica.2023.111158_b19 contributor: fullname: Rudin – volume: 95 start-page: 215 issue: 1 year: 2007 ident: 10.1016/j.automatica.2023.111158_b16 article-title: Consensus and cooperation in networked multi-agent systems publication-title: Proceedings of the IEEE doi: 10.1109/JPROC.2006.887293 contributor: fullname: Olfati-Saber |
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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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