Abstract
This paper deals with the consensus problem of dynamical networks of multi-agents with communication delays. The communication topology is assumed to be directed and connected. The intrinsic nonlinear dynamics are introduced to reflect more realistic dynamical behaviors of the agent systems. We propose a complete consensus protocols that take into account the weighted sum historical information exchange over a time interval \([t-\tau ,t]\). Using tools from differential equations, together with results from matrix theory and algebraic graph theory, sufficient conditions are derived to make all agents asymptotically achieve the consistency. Simulation results illustrate the theoretical results.
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References
Beard, R.W., Lawton, J., Hadaegh, F.Y.: A coordination architecture for spacecraft formation control. IEEE Trans. Control Syst. Technol. 9, 777–790 (2001)
Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51, 401–420 (2006)
Tanner, H., Jadbabaie, A., Pappas, G.J.: Flocking in fixed and switching networks. IEEE Trans. Autom. Control 52, 863–868 (2007)
Ren, W.: Multi-vehicle consensus with a time-varying reference state. Syst. Control Lett. 56, 474–483 (2007)
Li, Z., Duan, Z., Chen, G.: Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. Ieee trans. circuits syst. i regul. pap. 57, 213–224 (2010)
Hu, M., Yang, Y., Xu, Z.: Projective synchronization in drive-response dynamical networks. Phys. A Stat. Mech. Appl. 381, 457–466 (2007)
Papachristodoulou, A., Jadbabaie, A., Munz, U.: Effects of delay in multi-agent consensus and oscillator synchronization. IEEE Trans. Autom. Control 55, 1471–1477 (2010)
Dzhunusov, I.A., Fradkov, A.L.: Synchronization in networks of linear agents with output feedbacks. Autom. Remote Control 72, 1615–1626 (2011)
Yu, W., Chen, G., Cao, M.: Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans. Syst. Man Cybern. Part B Cybern. 40, 881–891 (2010)
Song, Q., Cao, J., Yu, W.: Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst. Control Lett. 59, 553–562 (2010)
Yu, W., Ren, W., Zheng, W.X.: Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49, 2107–2115 (2013)
Wang, H.: Consensus of networked mechanical systems with communication delays: a unified framework. IEEE Trans. Autom. Control 59, 1571–1576 (2014)
Nuno, E., Ortega, R., Basanez, L., Hill, D.: Synchronization of networks of nonidentical euler-lagrange systems with uncertain parameters and communication delays. IEEE Trans. Autom. Control 56, 935–941 (2011)
Yu, W., Chen, G.R., Cao, M.: Consensus in directed networks of agents with nonlinear dynamics. IEEE Trans. Autom. Control 56, 1436–1441 (2011)
Wang, B.C., Zhang, J.F.: Distributed control of multi-agent systems with random parameters and a major agent. Automatica 48, 2093–2106 (2012)
Cao, Y., Ren, W.: Multi-agent consensus using both current and outdated states with fixed and undirected interaction. J. Intell. Robot. Syst. 58(1), 95–106 (2010)
Kuang, Y.: Delay Differential Equations: with Applications in Population Dynamics. Academic Press, Boston (1993)
Liu, Y., Wang, Z., Liang, J.: Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38, 1314–1325 (2008)
Wan, X., Fang, H., Fu, S.: Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts. Appl. Math. Model. 36, 270–278 (2008)
Wu, Z.G., Shi, P., Su, H.: Reliable control for discrete-time fuzzy systems with infinite-distributed delay. IEEE Trans. Fuzzy Syst. 20, 22–31 (2012)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49, 1520–1533 (2004)
Bliman, P.A., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. Automatica 44, 1985–1995 (2008)
Wen, G., Duan, Z., Yu, W.: Consensus of multi-agent systems with nonlinear dynamics and sampled-data information. Int. J. Robust Nonlinear Control 23, 602–619 (2013)
Liu, J., Liu, X., Xie, W.C.: Stochastic consensus seeking with communication delays. Automatica 47, 2689–2696 (2011)
Liu, X., Chen, T.: Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix. Phys. A Stat. Mech. Appl. 387, 4429–4439 (2008)
Wang, Y., Cao, J.: Pinning synchronization of delayed neural networks with nonlinear inner-coupling. Discrete Dynamics in Nature and Society (2011)
Acknowledgments
This work was jointly supported by the National Natural Science Foundation of China under Grant 11202084, (Jiangnan University), Ministry of Education of China.
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Qiu, L., Guo, L., Liu, J., Yang, Y. (2016). A Distributed Delay Consensus of Multi-Agent Systems with Nonlinear Dynamics in Directed Networks. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_30
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DOI: https://doi.org/10.1007/978-3-319-40663-3_30
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