Kybernetika 59 no. 3, 461-483, 2023

Consensus of multi-agent systems and stabilization of large-scale systems with time delays and nonlinearities - a comparison of both problems

Branislav Rehák and Volodymyr LynnykDOI: 10.14736/kyb-2023-3-0461

Abstract:

The problem of stabilization of large-scale systems and the consensus problem of multi-agent systems are related, similar tools for their solution are used. Therefore, they are occasionally confused. Although both problems show similar features, one can also observe important differences. A comparison of both problems is presented in this paper. In both cases, attention is paid to the explanation of the effects of the time delays. The most important fact is that, if the time delays are heterogeneous, full synchronization of the multi-agent systems cannot be achieved; however, stabilization of the large-scale network is reachable. In the case of nonlinear systems, we show that the stabilization of a large-scale nonlinear system is possible under more restrictive assumptions compared to the synchronization of a nonlinear multi-agent system.

Keywords:

multi-agent systems, time delays, large-scale interconnected systems, nonlinearity

Classification:

93A14, 93B36

paper.pdf

References:

  1. G. Antonelli: Interconnected dynamic systems: An overview on distributed control. IEEE Control Systems 33 (2013), 1, 76-88.   DOI:10.1109/MCS.2012.2225929
  2. L. Bakule: Decentralized control: Status and outlook. Ann. Rev. Control 38 (2014), 71-80.   DOI:10.1016/j.arcontrol.2014.03.007
  3. L. Bakule, M. de la Sen, M. Papík and B. Rehák: Decentralized stabilization of complex systems with delayed feedback. In: Proc. 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications LSS, Shanghai 2013, pp. 31-36.   CrossRef
  4. L. Bakule, M. De la Sen, M. Papík and B. Rehák: Decentralized stabilization of symmetric systems with delayed observer-based feedback. In: Proc. American Control Conference 2013, pp. 6679-6684.   CrossRef
  5. L. Bakule, B. Rehák and M. Papík: Decentralized H-infinity control of complex systems with delayed feedback. Automatica 67 (2016), 127-131.   DOI:10.1016/j.automatica.2016.01.013
  6. N. Chen, G. Zhai, W. Gui, C. Yang and W. Liu: Decentralized H$_\infty$ quantisers design for uncertain interconnected networked systems. IET Control Theory Appl. 4 (2010), 177-185.   DOI:10.1049/iet-cta.2008.0580
  7. O. Demir and J. Lunze: Networked control of symmetrically interconnected systems. In: Proc. 19th Mediterranean Conference on Control and Automation, Corfu 2011, pp. 1014-1021, Corfu.   CrossRef
  8. O. Demir, J. Lunze and P. Otte: Analogies in the controller design for multi-agent and physically interconnected systems with identical subsystems. In: 20th Mediterranean Conference on Control Automation (MED) 2012, pp. 1037-1042.   CrossRef
  9. E. Fridman: Introduction to Time-Delay Systems. Birkhäuser, Basel 2015.   CrossRef
  10. W. Hou, M. Fu, H. Zhang and Z. Wu: Consensus conditions for general second-order multi-agent systems with communication delay. Automatica 75 (2017), 293-298.   DOI:10.1016/j.automatica.2016.09.042
  11. H. Khalil: Nonlinear Systems. Prentice Hall, New Jersey 2001.   CrossRef
  12. Z. Li, Z. Duan, G. Chen and L. Huang: Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Trans. Circuits Systems I: Regular Papers 57 (2010), 1, 213-224.   CrossRef
  13. P. Lin, K. Qin, H. Zhao and M. Sun: A new approach to average consensus problems with multiple time-delays and jointly-connected topologies. J. Franklin Inst. 349 (2012), 1, 293-304.   DOI:10.1016/j.jfranklin.2011.11.002
  14. J. Lunze: Feedback Control of Large-Scale Systems. Prentice Hall, Hemel Hempstead 1992.   CrossRef
  15. Z. Meng, T. Yang, G. Li, W. Ren and D. Wu: Synchronization of coupled dynamical systems: Tolerance to weak connectivity and arbitrarily bounded time-varying delays. IEEE Trans. Automat. Control 63 (2018), 6, 1791-1797.   DOI:10.1109/tac.2017.2754219
  16. W. Ni and D. Cheng: Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems Control Lett. 59 (2010), 3, 209-217.   DOI:10.1016/j.sysconle.2010.01.006
  17. A. Petrillo, A. Salvi, S. Santini and A. S. Valente: Adaptive synchronization of linear multi-agent systems with time-varying multiple delays. J. Franklin Inst. 354 (2017), 18, 8586-8605.   DOI:10.1016/j.jfranklin.2017.10.015
  18. W. Qian, Y. Gao, L. Wang and S. Fei: Consensus of multiagent systems with nonlinear dynamics and time-varying communication delays. Int. J. Robust Nonlinear Control 29 (2019), 6, 1926-1940.   DOI:10.1299/jsmemagazine.29.111\_201\_1
  19. B. Rehák: Observer design for a time delay system via the {Razumikhin} approach. Asian J. Control 19 (2017), 6, 2226-2231.   CrossRef
  20. B. Rehák: Wirtinger inequality-based control design for an interconnected large-scale system with sampled controls. In: 2019 Chinese Control Conference (CCC), pp. 09-1014.   DOI:10.23919/ChiCC.2019.8866449
  21. B. Rehák and V. Lynnyk: Network-based control of nonlinear large-scale systems composed of identical subsystems. J. Franklin Inst. 356 (2018).   CrossRef
  22. B. Rehák and V. Lynnyk: Decentralized networked stabilization of a nonlinear large system under quantization. IFAC-PapersOnLine 52 (2019), 20, 49-54.   CrossRef
  23. B. Rehák and V. Lynnyk: Synchronization of nonlinear complex networks with input delays and minimum-phase zero dynamics. In: 19th International Conference on Control, Automation and Systems (ICCAS), IEEE 2019, pp. 759-764.   DOI:10.23919/iccas47443.2019.8971535
  24. B. Rehák and V. Lynnyk: Synchronization of symmetric complex networks with heterogeneous time delays. In: 22nd International Conference on Process Control (PC19), 2019, pp. 68-73.   CrossRef
  25. B. Rehák and V. Lynnyk: Consensus of a multi-agent system with heterogeneous delays. Kybernetika 56 (2020), 363-381.   DOI:10.14736/kyb-2020-2-0363
  26. B. Rehák and V. Lynnyk: Synchronization of multi-agent systems with directed topologies and heterogeneous delays. In: European Control Conference ({ECC}), IEEE 2020, pp. 1671-1676.   DOI:10.23919/ecc51009.2020.9143705
  27. B. Rehák and V. Lynnyk: Leader-following synchronization of a multi-agent system with heterogeneous delays. Frontiers Inform. Technol. Electronic Engrg. 22 (2021), 1, 97-106.   DOI:10.2307/j.ctv1gt945c.10
  28. B. Rehák and V. Lynnyk: Approximate synchronization of complex network consisting of nodes with minimum-phase zero dynamics and uncertainties. IEEE Access 10 (2022), 35352-35362.   DOI:10.1109/access.2022.3163310
  29. B. Rehák, V. Lynnyk and S. Čelikovský: Consensus of homogeneous nonlinear minimum-phase multi-agent systems. IFAC-PapersOnLine 51 (2018), 13, 223-228.   CrossRef
  30. D. Wang, Z. Wang, M. Chen and W. Wang: Distributed optimization for multi-agent systems with constraints set and communication time-delay over a directed graph. Inform. Sci. 438 (2018), 1-14.   DOI:10.1038/s41574-018-0023-3
  31. H. {Wang}: Consensus of networked mechanical systems with communication delays: A unified framework. IEEE Trans. Automat. Control 59 (2014), 6, 1571-1576.   DOI:10.1109/tac.2013.2293413
  32. L. Zhang and G. Orosz: Consensus and disturbance attenuation in multi-agent chains with nonlinear control and time delays. Int. J. Robust Nonlinear Control 27 (2017), 5, 781-803.   DOI:10.1002/rnc.3600
  33. M. Zhang, A. Saberi and A. A. Stoorvogel: Synchronization in the presence of unknown, nonuniform and arbitrarily large communication delay. Europ. J. Control 38 (2017), :63-72.   DOI:10.1016/j.ejcon.2017.08.005