×

Consensus of high-order multi-agent systems with switching topologies. (English) Zbl 1406.93045

Summary: In this paper, a consensus problem is investigated for high-order multi-agent systems with switching communication networks, through which only output information instead of full-state information can be transmitted to neighbors. Based on self-state-feedback and neighbor-output-feedback, a new consensus protocol is proposed, which can realize arbitrary convergence rate. Furthermore, as an application, a nonlinear heading consensus protocol is designed for a multi-vehicle model. Finally, numerical simulations are given to illustrate the theoretical results.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C15 Control/observation systems governed by ordinary differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B35 Sensitivity (robustness)
93B52 Feedback control
90B18 Communication networks in operations research

Software:

Boids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Strogatz, S. H.; Stewart, I., Coupled oscillators and biological synchronization, Scientific American, 269, 102-109 (1993)
[2] Reynolds, C., Flocks, herds, and schools: A distributed behavioral model, Comput. Graph., 21, 25-34 (1987)
[3] Vicsek, T.; Czirok, A.; Ben-Jacob, E., Novel type of phase transitions in a system of self-driven particles, Phys. Rev. Lett., 75, 1226-1229 (1995)
[4] Kuramoto, Y., Self-entrainment of a population of coupled nonlinear oscillators, (Proceedings of International Symposium on Mathematical Problems in Theoretical Physics. Proceedings of International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physs., vol. 39 (1975)), 420-422
[5] Estrada, E., Path Laplacian matrices: Introduction and application to the analysis of consensus in networks, Linear Algebra Appl., 436, 3373-3391 (2012) · Zbl 1241.05077
[6] Abaid, N.; Igel, I.; Porfiri, M., On the consensus protocol of conspecific agents, Linear Algebra Appl., 437, 221-235 (2012) · Zbl 1238.93006
[7] De Lellis, P.; di Bernardo, M.; Garofalo, F.; Liuzza, D., Analysis and stability of consensus in networked control systems, Appl. Math. Comput., 217, 988-1000 (2010) · Zbl 1207.93007
[8] De Lellis, P.; Porfiri, M.; Bollt, E. M., Topological analysis of group fragmentation in multiagent systems, Phys. Rev. E, 87, 022818 (2013)
[9] Flierl, G.; Grunbaum, D.; Levin, S.; Olson, D., From individual to aggregation: The interplay between behavior and physics, J. Theoret. Biol., 196, 397-454 (1999)
[10] Bertsekas, D. P.; Tsitsiklis, J. N., Parallel and Distributed Computation: Numerical Methods (1989), Prentice Hall · Zbl 0743.65107
[11] Tsitsiklis, J. N.; Bertsekas, D. P.; Athans, M., Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE Trans. Automat. Control, 31, 803-812 (1986) · Zbl 0602.90120
[12] Chen, Y.; Lü, J.; Yu, X.; Hill, D. J., Multi-agent systems with dynamical topologies: Consensus and applications, IEEE Circuits Syst. Mag., 13, 21-34 (2013)
[13] Hegselmann, R.; Krause, U., Opinion dynamics and bounded confidence: Models, analysis and simulation, J. Artificial Soc. Social Simul., 5, 1-33 (2002)
[14] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48, 988-1001 (2003) · Zbl 1364.93514
[15] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 1520-1533 (2004) · Zbl 1365.93301
[16] Chopra, N.; Spong, M. W., On exponential synchronization of Kuramoto oscillators, IEEE Trans. Automat. Control, 54, 353-357 (2009) · Zbl 1367.34076
[17] Lin, Z.; Francis, B.; Maggiore, M., Necessary and sufficient graphical conditions for formation control of unicycles, IEEE Trans. Automat. Control, 50, 121-127 (2005) · Zbl 1365.93324
[18] Ren, W.; Beard, R. W., Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 655-661 (2005) · Zbl 1365.93302
[19] Olshevsky, A.; Tsitsiklis, J. N., On the nonexistence of quadratic Lyapunov functions for consensus algorithms, IEEE Trans. Automat. Control, 53, 2642-2645 (2008) · Zbl 1367.93611
[20] Chebotarev, P. Y.; Agaev, R. P., Coordination in multiagent systems and Laplacian spectra of digraphs, Autom. Remote Control, 70, 469-483 (2009) · Zbl 1163.93305
[21] Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, Internat. J. Robust Nonlinear Control, 17, 1002-1033 (2007) · Zbl 1266.93010
[22] Zhu, J.; Tian, Y.-P.; Kuang, J., On the general consensus protocol of multi-agent systems with double-integrator dynamics, Linear Algebra Appl., 431, 701-715 (2009) · Zbl 1165.93022
[23] Zhu, J., On consensus speed of multi-agent systems with double-integrator dynamics, Linear Algebra Appl., 434, 294-306 (2011) · Zbl 1201.93011
[24] Tuna, S. E., Synchronizing linear systems via partial-state coupling, Automatica, 44, 2179-2184 (2008) · Zbl 1283.93028
[25] Ma, C. Q.; Zhang, J. F., Necessary and sufficient conditions for consensusability of linear multi-agent systems, IEEE Trans. Automat. Control, 55, 1263-1268 (2010) · Zbl 1368.93383
[26] You, K.; Xie, L., Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE Trans. Automat. Control, 56, 2262-2275 (2011) · Zbl 1368.93014
[27] Chen, Y.; Lü, J.; Yu, X.; Lin, Z., Consensus of discrete-time second order multi-agent systems based on infinite products of general stochastic matrices, SIAM J. Control Optim., 51, 3274-3301 (2013) · Zbl 1275.93005
[28] Cao, M.; Morse, A. S.; Anderson, B. D.O., Reaching a consensus in a dynamically changing environment: Convergence rates, measurement delays, and asynchronous events, SIAM J. Control Optim., 42, 601-623 (2008) · Zbl 1157.93434
[29] Cao, M.; Morse, A. S.; Anderson, B. D.O., Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 42, 575-600 (2008) · Zbl 1157.93514
[30] Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents: Switching topology, (Proceedings of the 2006 American Control Conference (2006)), 1382-1387
[31] Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Trans. Syst. Man Cybern. B, 40, 881-891 (2010)
[32] Zhao, J.; Hill, D. J.; Liu, T., Synchronization of complex dynamical networks with switching topology: A switched system point of view, Automatica, 45, 2502-2511 (2009) · Zbl 1183.93032
[33] Lin, P.; Jia, Y.; Du, J.; Yu, F., Distributed leadless coordination for networks of second-order agents with time-delay on switching topology, (Proceedings of 2008 American Control Conference (2008)), 1564-1569
[34] Lin, P.; Jia, Y., Consensus of second-order discrete-time multiagent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 2154-2158 (2009) · Zbl 1175.93078
[35] Lin, P.; Jia, Y., Consensus of a class of second-order multiagent systems with time-delay and jointly-connected topologies, IEEE Trans. Automat. Control, 55, 778-784 (2010) · Zbl 1368.93275
[36] Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE Trans. Circuits Syst. I. Regul. Pap., 57, 213-224 (2010) · Zbl 1468.93137
[37] Watts, D. J.; Strogatz, S. H., Collective dynamics of ‘small-world’ networks, Nature, 393, 440-442 (1998) · Zbl 1368.05139
[38] Belykh, I. V.; Belykh, V. N.; Hasler, M., Blinking model and synchronization in small-world networks with a time-varying coupling, Phys. D, 195, 188-206 (2004) · Zbl 1098.82621
[39] Hasler, M.; Belykh, V.; Belykh, I., Dynamics of stochastically blinking systems. Part I: Finite time properties, SIAM J. Appl. Dyn. Syst., 12, 1007-1030 (2013) · Zbl 1285.34056
[40] Hasler, M.; Belykh, V.; Belykh, I., Dynamics of stochastically blinking systems. Part II: Asymptotic properties, SIAM J. Appl. Dyn. Syst., 12, 1031-1084 (2013) · Zbl 1285.34057
[41] Porfiri, M.; Stilwell, D. J.; Bollt, E. M.; Skufca, J. D., Random talk: Random walk and synchronizability in a moving neighborhood network, Phys. D, 224, 102-113 (2006) · Zbl 1115.60069
[42] Stilwell, D. J.; Bollt, E. M.; Roberson, D. G., Sufficient conditions for fast switching synchronization in time-varying network topologies, SIAM J. Appl. Dyn. Syst., 6, 140-156 (2006) · Zbl 1145.37345
[43] Abaid, N.; Porfiri, M., Leader-follower consensus over numerosity-constrained random networks, Automatica, 48, 1845-1851 (2012) · Zbl 1268.93005
[44] Zhou, J.; Wang, Q., Convergence speed in distributed consensus over dynamically switching random networks, Automatica, 45, 1455-1461 (2009) · Zbl 1166.93382
[45] Kar, S.; Moura, J. M.F., Distributed consensus algorithms in sensor networks with imperfect communication: Link failures and channel noise, IEEE Trans. Signal Process., 57, 355-369 (2009) · Zbl 1391.94263
[46] Qin, J.; Gao, H.; Zheng, W.-X., Second-order consensus for multi-agent systems with switching topology and communication delay, Systems Control Lett., 60, 390-397 (2011) · Zbl 1225.93020
[47] Zhu, J.; Lü, J.; Yu, X., Flocking of multi-agent non-holonomic systems with proximity graphs, IEEE Trans. Circuits Syst. I. Regul. Pap., 60, 199-210 (2013) · Zbl 1468.93047
[48] Lin, P.; Li, Z.; Jia, Y.; Sun, M., High-order multi-agent consensus with dynamically changing topologies and time-delays, IET Control Theory Appl., 5, 976-981 (2011)
[49] Yang, T.; Jin, Y.-H.; Wang, W.; Shi, Y.-J., Consensus of high-order continuous-time multi-agent systems with time-delays and switching topologies, Chinese Phys. B, 20, 020511 (2011)
[50] Godsil, C.; Royle, G., Algebraic Graph Theory (2001), Springer-Verlag: Springer-Verlag New York · Zbl 0968.05002
[51] Hong, Y.; Gao, L.; Cheng, D.; Hu, J., Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE Trans. Automat. Control, 52, 943-948 (2007) · Zbl 1366.93437
[52] Hu, G., Robust consensus tracking of a class of second-order multi-agent dynamic systems, Systems Control Lett., 61, 134-142 (2012) · Zbl 1250.93009
[53] Hu, G., Robust consensus tracking for an integrator-type multi-agent system with disturbances and unmodelled dynamics, Internat. J. Control, 84, 1-8 (2011) · Zbl 1221.93012
[54] Mellodge, P.; Kachroo, P., Model Abstraction in Dynamical Systems: Application to Mobile Robot Control Thesis, Lecture Notes in Control and Inform. Sci., vol. 379 (2008), Springer-Verlag · Zbl 1180.93002
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.