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Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation. (English) Zbl 1255.93010
Summary: By introducing delayed state compensation into the normal asynchronously-coupled consensus algorithm, a new consensus algorithm is constructed to solve the dynamical consensus problem of second-order multi-agent systems with communication delay. Based on frequency-domain analysis, a sufficient and necessary condition, which depends on the communication delay and the control parameters, is obtained for two coupled second-order dynamic agents converging to the dynamical consensus, and it is proved that the proposed algorithm can tolerate higher communication delay than the synchronously-coupled consensus algorithm. According to linear fractional transformation and the small-gain theorem, sufficient conditions are gained for second-order multi-agent systems with communication delay under a general digraph. Simulation results illustrates the correctness of our method.
MSC:
93A14Decentralized systems
68T42Agent technology (AI aspects)
93C80Frequency-response methods
References:
[1]Vicsek, T.; Czirok, A.; Jacob, E. B.; Cohen, I.; Schochet, O.: Novel type of phase transitions in a system of self-driven particles, Physical review letters 75, No. 6, 1226-1229 (1995)
[2]Jadbabaie, A.; Lin, J.; Morse, A. S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control 48, No. 6, 988-1001 (2003)
[3]Olfati-Saber, R.; Murray, R.: Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control 49, No. 9, 1520-1533 (2004)
[4]Ren, W.; Beard, R. W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control 50, No. 5, 655-661 (2005)
[5]Moreau, L.: Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control 50, No. 2, 169-182 (2005)
[6]Ren, W.; Atkins, E.: Distributed multi-vehicle coordinated control via local information exchange, International journal of robust and nonlinear control 17, No. 10–11, 1002-1033 (2007)
[7]Hong, Y. G.; Gao, L. X.; Cheng, D. Z.; Hu, J.: Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE transactions on automatic control 52, No. 5, 943-948 (2007)
[8]P. Lin, Y. Jia, J. Du, S. Yuan, Distributed consensus control for second-order agents with fixed topology and time-delay, in: Proceedings of the 26th Chinese Control Conference, 2007, pp. 577–581.
[9]Yu, W.; Chen, G.; Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica 46, No. 6, 1089-1095 (2010) · Zbl 1192.93019 · doi:10.1016/j.automatica.2010.03.006
[10]Hu, J.; Hong, Y.: Leader-following coordination of multi-agent systems with coupling time delays, Physica A 374, No. 2, 853-863 (2007)
[11]H. Su, X. Wang, Second-order consensus of multiple agents with coupling delay, in: Proceedings of the 7th World Congress on Intelligent Control and Automation, 2008, pp. 7181–7186.
[12]Lin, P.; Jia, Y.; Li, L.: Distributed robust H consensus control in directed networks of agents with time-delay, Systems control letters 57, No. 8, 643-653 (2008)
[13]Sun, Y. G.; Wang, L.; Xie, G.: Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems control letters 57, No. 2, 175-183 (2008) · Zbl 1133.68412 · doi:10.1016/j.sysconle.2007.08.009
[14]Qin, J.; Gao, H.; Zheng, W.: Second-order consensus for multi-agent systems with switching topology and communication delay, Systems control letters 60, No. 6, 390-397 (2011) · Zbl 1225.93020 · doi:10.1016/j.sysconle.2011.03.004
[15]Yu, J.; Wang, L.: Group consensus in multi-agent systems with switching topologies and communication delays, Systems control letters 59, No. 6, 340-348 (2010) · Zbl 1197.93096 · doi:10.1016/j.sysconle.2010.03.009
[16]C.-L. Liu, Y.-P. Tian, Consensus of multi-agent system with diverse communication delays, in: Proceedings of the 26th Chinese Control Conference, 2007, pp. 726–730.
[17]J. Wang, N. Elia, Consensus over network with dynamic channels, in: Proceedings of the 2008 American Control Conference, 2008, pp. 2637–2642.
[18]D.J. Lee, M.K. Spong, Agreement with non-uniform information delays, in: Proceedings of the 2006 American Control Conference, 2006, pp. 756–761.
[19]L. Moreau, Stability of continuous-time distributed consensus algorithms, in: Proceedings of the 43rd IEEE Conference on Decision and Control, 2004, pp. 3998–4003.
[20]Wang, W.; Slotine, J. J. E.: Contraction analysis of time-delayed communication delays, IEEE transactions on automatic control 51, No. 4, 712-717 (2006)
[21]Chopra, N.; Spong, M. K.: Passivity-based control of multi-agent systems, , 107-134 (2006)
[22]M. Cao, A.S. Morse, B.D.O. Anderson, Reaching an agreement using delayed information, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, pp. 3375–3380.
[23]L. Wang, F. Xiao, A new approach to consensus problems for discrete-time multi-agent systems with time-delays, in: Proceedings of the 2006 American Control Conference, 2006, pp. 2118–2123.
[24]Lin, P.; Jia, Y.: Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica 45, No. 9, 2154-2158 (2009) · Zbl 1175.93078 · doi:10.1016/j.automatica.2009.05.002
[25]Liu, C. -L.; Liu, F.: Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica 47, No. 9, 2130-2133 (2011) · Zbl 1227.93010 · doi:10.1016/j.automatica.2011.06.005
[26]W. Yang, A.L. Bertozzi, X.F. Wang, Stability of a second order consensus algorithm with time delay, in: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, pp. 2926–2931.
[27]Liu, C. -L.; Liu, F.: Asynchronously-coupled consensus of second-order dynamic agents with communication delay, International journal of innovative computing, information and control 6, No. 11, 5035-5046 (2010)
[28]Munz, U.; Papachristodoulou, A.; Allgower, F.: Delay robustness in consensus problems, Automatica 46, No. 8, 1252-1265 (2010) · Zbl 1204.93013 · doi:10.1016/j.automatica.2010.04.008
[29]Pyragas, K.: Continuous control of chaos by self-controlling feedback, Physics letters A 170, No. 6, 421-428 (1992)
[30]Lin, Z.; Francis, B.; Maggiore, M.: Necessary and sufficient graphical conditions for formation control of unicycles, IEEE transactions on automatic control 50, No. 1, 121-127 (2005)
[31]Liu, C. -L.; Liu, F.: Dynamical consensus seeking of heterogeneous multi-agent systems under input delays, International journal of communication systems (2012)