Kybernetika 56 no. 2, 363-381, 2020

Consensus of a multi-agent systems with heterogeneous delays

Branislav Rehák and Volodymyr LynnykDOI: 10.14736/kyb-2020-2-0363

Abstract:

The paper presents an algorithm for the solution of the consensus problem of a {linear }multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. {The control algorithm design is based on the $H_\infty$-control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number of agents, hence this problem is computationally tractable. } It is shown that heterogeneity {of the delays in the control loop} can cause a steady error in the synchronization. Magnitude of this error is estimated. The results are illustrated by two examples.

Keywords:

LMI, robust control, multi-agent system, time delay system

Classification:

93A14, 93B36

paper.pdf

References:

  1. A. Abdessameud, I. G. Polushin and A. Tayebi: Distributed coordination of dynamical multi-agent systems under directed graphs and constrained information exchange. IEEE Trans. Automat. Control 62 (2017), 4, 1668-1683.   CrossRef
  2. 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 2013, Shanghai, pp. 31-36, Shanghai.   DOI:10.1109/acc.2013.6580888
  3. L. Bakule, M. Papík and B. Rehák: Decentralized $H$-infinity control of complex systems with delayed feedback. Automatica 67 (2016), 127-131.   DOI:10.1016/j.automatica.2016.01.013
  4. N. Chen, G. Zhai, W. Gui, C. Yang and W. Liu: Decentralized Hinf quantisers design for uncertain interconnected networked systems. IET Control Theory Appl. 4 (2008), 177-183.   DOI:10.1016/j.automatica.2016.01.013
  5. G. Fiengo, D. Giuseppe Lui, A. Petrillo and S. Santini: Distributed leader-tracking adaptive control for high-order nonlinear lipschitz multi-agent systems with multiple time-varying communication delays. Int. J. Control (2019), 1-13.   CrossRef
  6. E. Fridman: Tutorial on Lyapunov-based methods for time-delay systems. Europ. J. Control 20 (204), 271-283.   DOI:10.1016/j.ejcon.2014.10.001
  7. E. Fridman: Introduction to Time-Delay Systems. Birkhäuser, Basel 2015.   CrossRef
  8. K. Hengster-Movric, F. L. Lewis, M. Šebek and T. Vyhlídal: Cooperative synchronization control for agents with control delays: A synchronizing region approach. J. Franklin Inst. 352 (2015), 5, 2002-2028.   DOI:10.1016/j.jfranklin.2015.02.011
  9. 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
  10. W. Hou, M. Y. Fu and H. Zhang: Consensusability of linear multi-agent systems with time delay. Int. J. Robust Nonlinear Control 26 (2015), 12, 2529-2541.   DOI:10.1002/rnc.3458
  11. L. Li, M. Fu, H. Zhang and R. Lu: Consensus control for a network of high order continuous-time agents with communication delays. Automatica 89 (2018), 144-150.   DOI:10.1016/j.automatica.2017.12.006
  12. Q. Li, B. Shen, Z. Wang, T. Huang and J. Luo: Synchronization control for a class of discrete time-delay complex dynamical networks: A dynamic event-triggered approach. IEEE Trans. Cybernet. 49 (2019), 5, 1979-1986.   DOI:10.1109/tcyb.2018.2818941
  13. Q. Li, Z. Wang, W. Sheng, F. E. Alsaadi and F. E. Alsaadi: Dynamic event-triggered mechanism for $h_{\infty}$ non-fragile state estimation of complex networks under randomly occurring sensor saturations. Inform. Sci. 509 (2020), 304-316.   DOI:10.1016/j.ins.2019.08.063
  14. 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.   DOI:10.1109/tcsi.2009.2023937
  15. P. Lin, M. Dai and Y. Song: Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays. J. Franklin Inst. 351 (2014), 3, 1571-1576.   DOI:10.1016/j.jfranklin.2013.11.015
  16. 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
  17. 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.   CrossRef
  18. A. Petrillo, A. Salvi, S. Santini and A. Saverio 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
  19. 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:10.1002/rnc.4471
  20. B. Rehák: Observer design for a time delay system via the Razumikhin approach. Asian J. Control 19 (2017), 6, 2226-2231.   DOI:10.1002/asjc.1507
  21. B. Rehák and V. Lynnyk: Network-based control of nonlinear large-scale systems composed of identical subsystems. J. Franklin Inst. 356 (2019), 2, 1088-1112.   DOI:10.1016/j.jfranklin.2018.05.008
  22. B. Rehák and V. Lynnyk: Synchronization of symmetric complex networks with heterogeneous time delays. In: 2019 22nd International Conference on Process Control (PC19), pp. 68-73.   DOI:10.1109/pc.2019.8815036
  23. X.-Y. Yao, H.-F. Ding and M.-F. Ge: Synchronization control for multiple heterogeneous robotic systems with parameter uncertainties and communication delays. J. Franklin Inst. 356 (2019), 16, 9713-9729.   DOI:10.1016/j.jfranklin.2018.10.041
  24. 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
  25. 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