Skip to main content

Trends and Questions in Open Multi-agent Systems

  • Chapter
  • First Online:
Hybrid and Networked Dynamical Systems

Abstract

This chapter presents a survey of recent trends in the analysis of open multi-agent systems, where the set of agents is time-varying. We first introduce the notions of arrivals, departures, and replacements of agents in the context of multi-agent systems, including several approaches for the modeling and time evolution. We then provide alternative definitions for concepts that must be adapted to conduct analyses in the open context, such as stability and convergence. We also consider some aspects of open systems that must be taken into account in the design of algorithms. Finally, some applications are presented to illustrate the current importance of open multi-agent systems as well as future perspectives in this framework.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Connected components of the graph associated with the HK dynamics.

  2. 2.

    This normalized norm is equivalent to the generalized mean defined for sets of numbers.

References

  1. Bullo, F.: Lectures on Network Systems, 1st ed. Kindle Direct Publishing (2022)

    Google Scholar 

  2. Moreau, L.: Stability of continuous-time distributed consensus algorithms. In: IEEE Conference on Decision and Control, vol. 4, pp. 3998–4003 (2004)

    Google Scholar 

  3. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  4. Lin, Z., Francis, B., Maggiore, M.: State agreement for continuous-time coupled nonlinear systems. SIAM J. Control Optim. 46(1), 288–307 (2007)

    Article  MathSciNet  Google Scholar 

  5. Monnoyer de Galland, C.: Open multi-agent systems: representation, limitations and decentralized optimization. Ph.D. dissertation, UCLouvain (2022)

    Google Scholar 

  6. Staedter, T.: 100,000 IoT sensors monitor a 1,400-km canal in China. IEEE Spectr. TechTalk Blog (2018)

    Google Scholar 

  7. Hauert, S., Bhatia, S.N.: Mechanisms of cooperation in cancer nanomedicine: towards systems nanotechnology. Trends Biotechnol. 32(9), 448–455 (2014)

    Article  Google Scholar 

  8. Claes, R., Holvoet, T., Weyns, D.: A decentralized approach for anticipatory vehicle routing using delegate multiagent systems. IEEE Trans. Intell. Transp. Syst. 12(2), 364–373 (2011)

    Article  Google Scholar 

  9. Proskurnikov, A., Tempo, R.: A tutorial on modeling and analysis of dynamic social networks. Part I. Ann. Rev. in Control 43, 65–79 (2017). (05)

    Google Scholar 

  10. Argente, E., Botti, V., Carrascosa, C., Giret, A., Julián, V., Rebollo, M.: An abstract architecture for virtual organizations: the Thomas approach. Knowl. Inf. Syst. 29, 379–403 (2011). (11)

    Google Scholar 

  11. Giret, A., Julián, V., Rebollo, M., Argente, E., Carrascosa, C., Botti, V.: An open architecture for service-oriented virtual organizations. Lect. Notes Comput. Sci. 5919(09), 118–132 (2010)

    Article  Google Scholar 

  12. Riverso, S., Farina, M., Ferrari-Trecate, G.: Plug-and-play decentralized model predictive control. In: IEEE Conference on Decision and Control, pp. 4193–4198 (2012)

    Google Scholar 

  13. Riverso, S., Farina, M., Ferrari-Trecate, G.: Plug-and-play state estimation and application to distributed output-feedback model predictive control. Eur. J. Control 25, 04 (2015)

    Article  MathSciNet  Google Scholar 

  14. Farina, M., Carli, R.: Partition-based distributed Kalman filter with plug and play features. IEEE Trans. Control Netw. Syst. 5(1), 560–570 (2018)

    Article  MathSciNet  Google Scholar 

  15. Huynh, T.D., Jennings, N.R., Shadbolt, N.R.: An integrated trust and reputation model for open multi-agent systems. Auton. Agents Multi-Agent Syst. 13(2), 119–154 (2006)

    Article  Google Scholar 

  16. Lykouris, T., Syrgkanis, V., Tardos, É.: Learning and efficiency in games with dynamic population. In: Proceedings of the Twenty-seventh Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, pp. 120–129 (2016)

    Google Scholar 

  17. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Ruppert, E.: When birds die: making population protocols fault-tolerant. In: International Conference on Distributed Computing in Sensor Systems. Springer pp. 51–66 (2006)

    Google Scholar 

  18. Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Principles of Distributed Systems, pp. 103–117. Springer, Berlin Heidelberg (2006)

    Google Scholar 

  19. Brasseur, B.: Algorithms in open multi-agent systems: gossiping with random replacements. In: Hendrickx, J.M. (ed.) Ecole polytechnique de Louvain, Université catholique de Louvain, 2018, prom (2018). http://hdl.handle.net/2078.1/thesis:16470

  20. Abdelrahim, M., Hendrickx, J.M., Heemels, W.: Max-consensus in open multi-agent systems with gossip interactions. In: IEEE Conference on Decision and Control, pp. 4753–4758 (2017)

    Google Scholar 

  21. Hendrickx, J.M., Martin, S.: Open multi-agent systems: gossiping with deterministic arrivals and departures. In: 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1094–1101 (2016)

    Google Scholar 

  22. Nedić, A., Olshevsky, A., Rabbat, M.G.: Network topology and communication-computation tradeoffs in decentralized optimization. Proc. IEEE 106, 953–976 (2018)

    Article  Google Scholar 

  23. Molinari, F., Raisch, J.: Efficient consensus-based formation control with discrete-time broadcast updates. In: IEEE Conference on Decision and Control, pp. 4172–4177 (Dec 2019)

    Google Scholar 

  24. Török, J., Iñiguez, G., Yasseri, T., San Miguel, M., Kaski, K., Kertész, J.: Opinions, conflicts, and consensus: modeling social dynamics in a collaborative environment. Phys. Rev. Lett. 110(8), 088701 (2013)

    Google Scholar 

  25. Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)

    Article  MathSciNet  Google Scholar 

  26. Ravazzi, C., Dabbene, F., Lagoa, C., Proskurnikov, A.V.: Learning hidden influences in large-scale dynamical social networks: a data-driven sparsity-based approach, in memory of Roberto tempo. IEEE Control Syst. Mag. 41(5), 61–103 (2021)

    Article  MathSciNet  Google Scholar 

  27. Proskurnikov, A.V., Tempo, R.: A tutorial on modeling and analysis of dynamic social networks. Part II. Ann. Rev. Control 45, 166–190 (2018)

    Article  MathSciNet  Google Scholar 

  28. Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002)

    Google Scholar 

  29. Grauwin, S., Jensen, P.: Opinion group formation and dynamics: structures that last from nonlasting entities. Phys. Rev. E 85, 066113 (Jun 2012)

    Google Scholar 

  30. Vizuete, R., Frasca, P., Panteley, E.: On Lyapunov functions for open Hegselmann-Krause dynamics (2023). arXiv:2303.07074

  31. Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.: Continuous-time average-preserving opinion dynamics with opinion-dependent communications. SIAM J. Control Opti. 48(8), 5214–5240 (2010)

    Article  MathSciNet  Google Scholar 

  32. Nowzari, C., Preciado, V.M., Pappas, G.J.: Analysis and control of epidemics: a survey of spreading processes on complex networks. IEEE Control Syst. Mag. 36(1), 26–46 (2016)

    Article  MathSciNet  Google Scholar 

  33. Alamo, T., Millán, P., Reina, D.G., Preciado, V.M., Giordano, G.: Challenges and future directions in pandemic control. IEEE Control Syst. Lett. 6, 722–727 (2022)

    Article  Google Scholar 

  34. Tizzoni, M., Bajardi, P., Decuyper, A., Kon Kam King, G., Schneider, C.M., Blondel, V., Smoreda, Z., González, M.C., Colizza, V.: On the use of human mobility proxies for modeling epidemics. PLoS Comput. Biol. 10(7), e1003716 (2014)

    Google Scholar 

  35. Hazarie, S., Soriano-Paños, D., Arenas, A., Gómez-Gardeñes, J., Ghoshal, G.: Interplay between population density and mobility in determining the spread of epidemics in cities. Commun. Phys. 4(1), 1–10 (2021)

    Article  Google Scholar 

  36. Ogura, M., Preciado, V.M.: Stability of spreading processes over time-varying large-scale networks. IEEE Trans. Netw. Sci. Eng. 3(1), 44–57 (2016)

    Article  MathSciNet  Google Scholar 

  37. Paré, P.E., Beck, C.L., Nedić, A.: Epidemic processes over time-varying networks. IEEE Trans. Control Netw. Syst. 5(3), 1322–1334 (2018)

    Article  MathSciNet  Google Scholar 

  38. Vizuete, R.: Contributions to open multi-agent systems: consensus, optimization and epidemics. Ph.D. dissertation, Université Paris-Saclay (2022)

    Google Scholar 

  39. Varma, V.S., Morărescu, I.-C., Nešić, D.: Open multi-agent systems with discrete states and stochastic interactions. IEEE Control Syst. Lett. 2(3), 375–380 (2018)

    Article  MathSciNet  Google Scholar 

  40. Hsieh, Y.-G., Iutzeler, F., Malick, J., Mertikopoulos, P.: Optimization in open networks via dual averaging. In: IEEE Conference on Decision and Control, pp. 514–520 (2021)

    Google Scholar 

  41. Monnoyer de Galland, C., Vizuete, R., Hendrickx, J.M., Panteley, E., Frasca, P.: Random coordinate descent for resource allocation in open multi-agent systems (2022). arXiv:2205.10259

  42. Verriest, E.I.: Multi-mode multi-dimensional systems. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, pp. 1268–1274 (2006)

    Google Scholar 

  43. Verriest, E.I.: Pseudo-continuous multi-dimensional multi-mode systems. Discrete Event Dyn. Syst. 22(1), 27–59 (2012)

    Article  MathSciNet  Google Scholar 

  44. Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid Dynamical Systems. Princeton University Press (2012)

    Google Scholar 

  45. Lovász, L.: Large Networks and Graph Limits. American Mathematical Society, vol. 60 (2012)

    Google Scholar 

  46. Avella-Medina, M., Parise, F., Schaub, M.T., Segarra, S.: Centrality measures for graphons: accounting for uncertainty in networks. IEEE Trans. Netw. Sci. Eng. 7(1), 520–537 (2020)

    Article  MathSciNet  Google Scholar 

  47. Gao, S., Caines, P.E.: Graphon control of large-scale networks of linear systems. IEEE Trans. Autom. Control 65(10), 4090–4105 (2020)

    Article  MathSciNet  Google Scholar 

  48. Delmas, J.-F., Dronnier, D., Zitt, P.-A.: An infinite-dimensional metapopulation sis model. J. Differ. Equ. 313, 1–53 (2022)

    Article  MathSciNet  Google Scholar 

  49. Noroozi, N., Mironchenko, A., Kawan, C., Zamani, M.: Small-gain theorem for stability, cooperative control and distributed observation of infinite networks (2020). arXiv:2002.07085

  50. Monnoyer de Galland, C., Martin, S., Hendrickx, J.M.: Modelling gossip interactions in open multi-agent systems (2020). arXiv:2009.02970

  51. Franceschelli, M., Frasca, P.: Stability of open multi-agent systems and applications to dynamic consensus. IEEE Trans. Autom. Control 66(5), 2326–2331 (2021)

    Article  Google Scholar 

  52. Vizuete, R., Monnoyer de Galland, C., Hendrickx, J.M., Frasca, P., Panteley, E.: Resource allocation in open multi-agent systems: an online optimization analysis. In: IEEE Conference on Decision and Control, pp. 5185–5191 (2022)

    Google Scholar 

  53. Dörfler, F., Bullo, F.: Synchronization in complex networks of phase oscillators: a survey. Automatica 50(6), 1539–1564 (2014)

    Article  MathSciNet  Google Scholar 

  54. Teel, A.R., Hespanha, J.P.: Stochastic hybrid systems: a modeling and stability theory tutorial. In: IEEE Conference on Decision and Control, pp. 3116–3136 (2015)

    Google Scholar 

  55. Xue, M., Tang, Y., Ren, W., Qian, F.: Stability of multi-dimensional switched systems with an application to open multi-agent systems. Automatica 146, 110644 (2022)

    Article  MathSciNet  Google Scholar 

  56. Hendrickx, J.M., Martin, S.: Open multi-agent systems: gossiping with random arrivals and departures. In: IEEE Conference on Decision and Control, pp. 763–768 (2017)

    Google Scholar 

  57. Brockett, R.: Stochastic Control. Harvard University, Lecture Notes (2009)

    Google Scholar 

  58. Brockett, R., Gong, W., Guo, Y.: Stochastic analysis for fluid queueing systems. In: IEEE Conference on Decision and Control, vol. 3, pp. 3077–3082 (1999)

    Google Scholar 

  59. Privault, N.: Stochastic Finance: An Introduction with Market Examples. CRC Press (2013)

    Google Scholar 

  60. Jacobsen, M.: Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes. Birkhäuser Boston (2006)

    Google Scholar 

  61. Colla, S.: Data fusion in open multi-agent systems for decentralized estimation. Hendrickx, J.M. (ed.) Ecole polytechnique de Louvain, Université catholique de Louvain, 2020, prom (2020). https://dial.uclouvain.be/memoire/ucl/object/thesis:25154

  62. Monnoyer de Galland, C., Hendrickx, J.M.: Fundamental performance limitations for average consensus in open multi-agent systems. IEEE Trans. Autom. Control (2022)

    Google Scholar 

  63. Sanai Dashti, Z.A.Z., Seatzu, C., Franceschelli, M.: Dynamic consensus on the median value in open multi-agent systems. In: IEEE Conference on Decision and Control, pp. 3691–3697 (2019)

    Google Scholar 

  64. Deplano, D., Franceschelli, M., Giua, A.: Dynamic min and max consensus and size estimation of anonymous multiagent networks. IEEE Trans. Autom. Control 68(1), 202–213 (2023)

    Article  MathSciNet  Google Scholar 

  65. Vizuete, R., Frasca, P., Panteley, E.: On the influence of noise in randomized consensus algorithms. IEEE Control Syst. Lett. 5(3), 1025–1030 (2021)

    Article  MathSciNet  Google Scholar 

  66. Simonetto, A., Dall’Anese, E., Paternain, S., Leus, G., Giannakis, G.B.: Time-varying convex optimization: time-structured algorithms and applications. Proc. IEEE 108(11), 2032–2048 (2020)

    Article  Google Scholar 

  67. Hendrickx, J.M., Rabbat, M.G.: Stability of decentralized gradient descent in open multi-agent systems. In: IEEE Conference on Decision and Control, pp. 4885–4890 (2020)

    Google Scholar 

  68. Vizuete, R., Frasca, P., Panteley, E.: Gradient descent for resource allocation with packet loss. IFAC-PapersOnLine 55(13), 109–114 (2022)

    Article  Google Scholar 

  69. Sun, Y., Fernando, H., Chen, T., Shahrampour, S.: On the stability analysis of open federated learning systems. In: American Control Conference, pp. 867–872. IEEE (2023)

    Google Scholar 

  70. Hazan, E.: Introduction to online convex optimization. Found. Trends Opti. 2, 157–325 (2016)

    Article  Google Scholar 

  71. Bubeck, S.: Introduction to online optimization (Dec 2011). https://www.microsoft.com/en-us/research/publication/introduction-online-optimization/

  72. Nakamura, T., Hayashi, N., Inuiguchi, M.: Cooperative learning for adversarial multi-armed bandit on open multi-agent systems. IEEE Control Syst. Lett. 7, 1712–1717 (2023)

    Article  MathSciNet  Google Scholar 

  73. Claes, R., Holvoet, T., Weyns, D.: A decentralized approach for anticipatory vehicle routing using delegate multiagent systems. IEEE Trans. Intell. Transp. Syst. 12(2), 364–373 (2011)

    Article  Google Scholar 

  74. Tonguz, O.K.: Red light, green light-no light: tomorrow’s communicative cars could take turns at intersections. IEEE Spectr. 55(10), 24–29 (2018)

    Article  Google Scholar 

  75. Hamann, H.: Swarm Robotics: A Formal Approach, vol. 221. Springer (2018)

    Google Scholar 

  76. Valentini, G.: Achieving Consensus in Robot Swarms, vol. 706. Springer (2017)

    Google Scholar 

  77. Restrepo, E., Loría, A., Sarras, I., Marzat, J.: Consensus of open multi-agent systems over dynamic undirected graphs with preserved connectivity and collision avoidance. In: IEEE Conference on Decision and Control, pp. 4609–4614 (2022)

    Google Scholar 

  78. Vizuete, R., Frasca, P., Garin, F.: Graphon-based sensitivity analysis of SIS epidemics. IEEE Control Syst. Lett. 4(3), 542–547 (2020)

    Article  MathSciNet  Google Scholar 

  79. Vizuete, R., Garin, F., Frasca, P.: The Laplacian spectrum of large graphs sampled from graphons. IEEE Trans. Netw. Sci. Eng. 8(2), 1711–1721 (2021)

    Article  MathSciNet  Google Scholar 

  80. Bonnet, B., Duteil, N.P., Sigalotti, M.: Consensus formation in first-order graphon models with time-varying topologies. In: Mathematical Models and Methods in Applied Sciences (2022)

    Google Scholar 

  81. Bramburger, J., Holzer, M.: Pattern formation in random networks using graphons. SIAM J. Math. Anal. 55(3), 2150–2185 (2023)

    Article  MathSciNet  Google Scholar 

  82. Fagnani, F., Frasca, P.: Introduction to Averaging Dynamics over Networks. Springer, Cham, Switzerland (2018)

    Book  Google Scholar 

  83. Bollobás, B.: Random Graphs, 2nd ed. Cambridge University Press (2001)

    Google Scholar 

  84. Stüdli, S., Yan, Y., Seron, M.M., Middleton, R.H.: Plug-and-play network reconfiguration algorithms to maintain regularity and low network reconfiguration needs. IEEE Control Syst. Lett. 6, 3451–3456 (2022)

    Google Scholar 

  85. Abad Torres, J., Cruz, P.J., Vizuete, R., Fierro, R.: On resilience and heterogeneity in robotic networks. In: Cooperative Localization and Navigation, pp. 141–158. CRC Press (2019)

    Google Scholar 

  86. Panteley, E., Loría, A.: Synchronization and dynamic consensus of heterogeneous networked systems. IEEE Trans. Autom. Control 62(8), 3758–3773 (2017)

    Article  MathSciNet  Google Scholar 

  87. Maghenem, M., Panteley, E., Loría, A.: Singular-perturbations-based analysis of dynamic consensus in directed networks of heterogeneous nonlinear systems (2022). arXiv:2205.15646

  88. Adhikari, B., Morărescu, I.-C., Panteley, E.: An emerging dynamics approach for synchronization of linear heterogeneous agents interconnected over switching topologies. IEEE Control Syst. Lett. 5(1), 43–48 (2021)

    Article  MathSciNet  Google Scholar 

  89. Teel, A.R., Subbaraman, A., Sferlazza, A.: Stability analysis for stochastic hybrid systems: a survey. Automatica 50(10), 2435–2456 (2014)

    Article  MathSciNet  Google Scholar 

  90. Rossi, W.S., Frasca, P.: Asynchronous opinion dynamics on the \(k\)-nearest-neighbors graph. In: IEEE Conference on Decision and Control, pp. 3648–3653 (2018)

    Google Scholar 

Download references

Acknowledgements

This work was supported by F.R.S.-FNRS via the KORNET project and via the Incentive Grant for Scientific Research (MIS) Learning from Pairwise Comparisons, and by the RevealFlight Concerted Research Action (ARC) of the Fédération Wallonie-Bruxelles and in part by the “Agence Nationale de la Recherche” (ANR) under Grant HANDY ANR-18-CE40-0010. R. Vizuete is a FNRS Postdoctoral Researcher – CR.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renato Vizuete .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vizuete, R., Monnoyer de Galland, C., Frasca, P., Panteley, E., Hendrickx, J.M. (2024). Trends and Questions in Open Multi-agent Systems. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-49555-7_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49554-0

  • Online ISBN: 978-3-031-49555-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics