Consensus for multiagent systems with nonlinear dynamics and time delays using a two-hop relay adaptive method. (English) Zbl 1406.93016

Summary: This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results.


93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C10 Nonlinear systems in control theory
93C40 Adaptive control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
Full Text: DOI


[1] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301
[2] Blondel, V. D.; Hendrickx, J. M.; Olshevsky, A.; Tsitsiklis, J. N., Convergence in multiagent coordination, consensus, and flocking, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC ’05)
[3] Lasseter, R. H., MicroGrids, Proceedings of the IEEE Power Engineering Society Winter Meeting
[4] Ren, W.; Atkins, E., Second-order consensus protocols in multiple vehicle systems with local interactions, Proceedings of the AIAA Guidance, Navigation, and Control Conference
[5] Yu, W.; Zheng, W. X.; Chen, G.; Ren, W.; Cao, J., Second-order consensus in multi-agent dynamical systems with sampled position data, Automatica, 47, 7, 1496-1503 (2011) · Zbl 1220.93005
[6] Yang, H.; Zhang, Z.; Zhang, S., Consensus of second-order multi-agent systems with exogenous disturbances, International Journal of Robust and Nonlinear Control, 21, 9, 945-956 (2011) · Zbl 1215.93014
[7] Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019
[8] Lin, P.; Dai, M.; Song, Y., Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays, Journal of the Franklin Institute, 351, 3, 1571-1576 (2014) · Zbl 1395.93054
[9] Tian, Y.-P.; Liu, C.-L., Consensus of multi-agent systems with diverse input and communication delays, IEEE Transactions on Automatic Control, 53, 9, 2122-2128 (2008) · Zbl 1367.93411
[10] Lin, P.; Jia, Y., Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 9, 2154-2158 (2009) · Zbl 1175.93078
[11] Yin, S.; Wang, G.; Karimi, H. R., Data-driven design of robust fault detection system for wind turbines, Mechatronics (2013)
[12] Yin, S.; Ding, S.; Haghani, A.; Hao, H., Data-driven monitoring for stochastic systems and its application on batch process, International Journal of Systems Science, 44, 7, 1366-1376 (2013) · Zbl 1278.93259
[13] Feng, X.; Long, W., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Transactions on Automatic Control, 53, 8, 1804-1816 (2008) · Zbl 1367.93255
[14] Nuño, E.; Ortega, R.; Basañez, L.; Hill, D., Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays, IEEE Transactions on Automatic Control, 56, 4, 935-941 (2011) · Zbl 1368.93308
[15] Bidram, A.; Davoudi, A.; Lewis, F. L.; Guerrero, J. M., Distributed cooperative secondary control of microgrids using feedback linearization, IEEE Transactions on Power Systems, 28, 3, 3462-3470 (2013)
[16] Zhihua, Q.; Jing, W.; Hull, R. A., Cooperative control of dynamical systems with application to autonomous vehicles, IEEE Transactions on Automatic Control, 53, 4, 894-911 (2008) · Zbl 1367.93076
[17] Li, H.; Liao, X.; Huang, T.; Wang, Y.; Han, Q.; Dong, T., Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies, Information Sciences, 259, 25-35 (2014) · Zbl 1332.34094
[18] Qian, Y.; Wu, X.; Lü, J.; Lu, J.-A., Second-order consensus of multi-agent systems with nonlinear dynamics via impulsive control, Neurocomputing, 125, 142-147 (2014)
[19] Yu, H.; Xia, X., Adaptive consensus of multi-agents in networks with jointly connected topologies, Automatica, 48, 8, 1783-1790 (2012) · Zbl 1267.93007
[20] Yin, S.; Luo, H.; Ding, S., Real-time implementation of fault-tolerant control systems with performance optimization, IEEE Transactions on Industrial Electronics, 61, 5, 2402-2411 (2014)
[21] Yin, S.; Ding, S. X.; Haghani, A.; Hao, H.; Zhang, P., A comparison study of basic datadriven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process, Journal of Process Control, 22, 9, 1567-1581 (2012)
[22] Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Transactions on Systems, Man, and Cybernetics B, 40, 3, 881-891 (2010)
[23] Wen, G. H.; Duan, Z. S.; Yu, W. W.; Chen, G. R., Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications, International Journal of Control, 86, 2, 322-331 (2013) · Zbl 1278.93016
[24] Wu, C. W.; Chua, L. O., Synchronization in an array of linearly coupled dynamical systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42, 8, 430-447 (1995) · Zbl 0867.93042
[25] Zhipu, J.; Murray, R. M., Multi-hop relay protocols for fast consensus seeking, Proceedings of the 45th IEEE Conference on Decision and Control
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.