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Keywords:
multi-agent system; time delay system; robust control; LMI
multi-agent system; time delay system; robust control; LMI
Summary:
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.
References:
[1] Abdessameud, A., Polushin, I. G., Tayebi, A.: Distributed coordination of dynamical multi-agent systems under directed graphs and constrained information exchange. IEEE Trans. Automat. Control 62 (2017), 4, 1668-1683. DOI 10.1109/TAC.2016.2609498 | MR 3636325
[2] Bakule, L., Sen, M. de la, Papík, M., Rehák, B.: 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] Bakule, L., Papík, M., Rehák, B.: Decentralized $H$-infinity control of complex systems with delayed feedback. Automatica 67 (2016), 127-131. DOI 10.1016/j.automatica.2016.01.013 | MR 3471755
[4] Chen, N., Zhai, G., Gui, W., Yang, C., Liu, W.: 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 | MR 2640374
[5] Fiengo, G., Lui, D. Giuseppe, Petrillo, A., Santini, S.: 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. DOI 10.1080/00207179.2019.1683608
[6] Fridman, E.: Tutorial on Lyapunov-based methods for time-delay systems. Europ. J. Control 20 (204), 271-283. DOI 10.1016/j.ejcon.2014.10.001 | MR 3283869
[7] Fridman, E.: Introduction to Time-Delay Systems. Birkhäuser, Basel 2015. MR 3237720
[8] Hengster-Movric, K., Lewis, F. L., Šebek, M., Vyhlídal, T.: 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 | MR 3334125
[9] Hou, W., Fu, M., Zhang, H., Wu, Z.: 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 | MR 3582183
[10] Hou, W., Fu, M. Y., Zhang, H.: Consensusability of linear multi-agent systems with time delay. Int. J. Robust Nonlinear Control 26 (2015), 12, 2529-2541. DOI 10.1002/rnc.3458 | MR 3520920
[11] Li, L., Fu, M., Zhang, H., Lu, R.: 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 | MR 3762042
[12] Li, Q., Shen, B., Wang, Z., Huang, T., Luo, J.: 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 | MR 3891660
[13] Li, Q., Wang, Z., Sheng, W., Alsaadi, F. E., Alsaadi, F. E.: 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 | MR 4009557
[14] Li, Z., Duan, Z., Chen, G., Huang, L.: 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 | MR 2729823
[15] Lin, P., Dai, M., Song, Y.: 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 | MR 3165212
[16] Lin, P., Qin, K., Zhao, H., Sun, M.: 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 | MR 2874739
[17] Meng, Z., Yang, T., Li, G., Ren, W., Wu, D.: 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 | MR 3807661
[18] Petrillo, A., Salvi, A., Santini, S., Valente, A. Saverio: 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 | MR 3732306
[19] Qian, W., Gao, Y., Wang, L., Fei, S.: 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 | MR 3934402
[20] Rehák, B.: Observer design for a time delay system via the Razumikhin approach. Asian J. Control 19 (2017), 6, 2226-2231. DOI 10.1002/asjc.1507 | MR 3730209
[21] Rehák, B., Lynnyk, V.: 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 | MR 3912566
[22] Rehák, B., Lynnyk, V.: 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] Yao, X.-Y., Ding, H.-F., Ge, M.-F.: 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 | MR 4025644
[24] Zhang, L., Orosz, G.: 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 | MR 3608606
[25] Zhang, M., Saberi, A., Stoorvogel, A. A.: 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 | MR 3719912
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