Leader-following consensus of multi-agent systems under fixed and switching topologies. (English) Zbl 1223.93006

Summary: The leader-following consensus problem of higher order multi-agent systems is considered. The dynamics of each agent and the leader is assumed as a linear system. The control of each agent using local information is designed and a detailed analysis of the leader-following consensus is presented for both fixed and switching interaction topologies, which describe the information exchange between the multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and Lyapunov inequality. Simulations indicate the capabilities of the algorithms.


93A14 Decentralized systems
93C35 Multivariable systems, multidimensional control systems
93B25 Algebraic methods
Full Text: DOI


[1] Lian, Z.; Deshmukh, A., Performance prediction of an unmanned airborn vehicle multi-agent system, European journal of operational research, 172, 2, 680-695, (2006) · Zbl 1168.90669
[2] Lin, Z.; Francis, B.; Maggiore, M., Necessary and sufficient graphical conditions for formation control of unicycles, IEEE transactions on automatic control, 50, 1, 121-127, (2005) · Zbl 1365.93324
[3] J. Lin, A.S. Morse, B.D.O. Anderson, The multi-agent rendezvous problem, in: Proceedings of 42nd IEEE Conference on Decision and Control, vol. 2 (9) 2003, pp. 1508-1513.
[4] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[5] R. Olfati-Saber, J.S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, in: Procceedings of 44th IEEE Conference on Decision and Control, and the European Control Conference, 2005, pp. 6698-6703.
[6] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 943-948, (2007)
[7] Vicsek, T.; Czirok, A.; Jacob, E.B.; Cohen, I.; Schochet, O., Novel type of phase of phase trasitions in a system of self-dedriven particles, Physical review letters, 75, 6, 1226-1229, (1995)
[8] Savkin, A.V., Coordinated collective motion of groups of autonomous mobile robots: analysis of vicsek’s model, IEEE transactions on automatic control, 49, 6, 981-983, (2004) · Zbl 1365.93327
[9] H.G. Tanner, A. Jadbabaie, G.J. Pappas, Stable flocking of mobile agents, Part I: Fixed topology; Part II: Dynamic topology, in: Proceedings of 42nd IEEE Conference on Decision and Control, 2, 2003, pp. 2010-2015, pp. 2016-2021.
[10] Lin, Z.; Brouchke, M.; Francis, B., Local control strategies for a groups of mobile atutonomous agents, IEEE transactions on automatic control, 49, 4, 622-629, (2004) · Zbl 1365.93208
[11] W. Ren, R.W. Beard, Consensus of information under dyanmically changing interaction topologies, in: Preccedings of the 2004 Americian Control Conference, Boston, MA, 2004, pp. 4939-4944.
[12] R. Olfati-Saber, R.M. Murray, Consensus protocols for networks of dynamic agents, in: Proceedings of 2003 American Control Conference, 2003.
[13] 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
[14] Hatano, Y.; Medbshi, M., Agreement over random networks, IEEE transactions on automatic control, 50, 11, 1867-1872, (2005) · Zbl 1365.94482
[15] Huang, M.; Manton, J.H., Coordination and consensus of networked agents with noisy measurents: stochastic algorithms and asymptotic behavior, SIAM journal on control and optimization, 48, 1, 134-161, (2009) · Zbl 1182.93108
[16] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[17] Tian, Y.; Liu, C., Consensus of multi-agent systems with diverse input and communication delays, IEEE transactions on automatic control, 53, 9, 2122-2128, (2008) · Zbl 1367.93411
[18] Godsil, C.; Royle, G., Algebraic graph theory, (2001), Spinger-verlag New York · Zbl 0968.05002
[19] Hong, Y.; Gao, L.; Cheng, D.; Hu, J., Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE transactions on automatic control, 52, 5, 943-948, (2007) · Zbl 1366.93437
[20] Q. Hui, W.M. Haddad, S.P. Bhat, Finite-time semistability theory with applications to consensus protocols in dynamical networks, in: Proceedings of 2007 American Control Conference, 2007, pp. 2411-2416.
[21] Pham, Q.; Slotine, J.J., Stable concurrent sysnchronization in dynamical system networks, Neural networks, 20, 1, 62-77, (2007)
[22] Slotine, J.J.E.; Wang, W., A study of synchronization and group cooperation using partial contraction theory, ()
[23] Wang, W.; Slotine, J.J.E., Contraction analysis of time-delayed communications and group cooperation, IEEE transactions on automatic control, 51, 4, 712-717, (2006) · Zbl 1366.90064
[24] Acrak, M., Passivity as a design tool for group coordination, IEEE transactions on automatic control, 52, 8, 1380-1390, (2007) · Zbl 1366.93563
[25] Chopra, N.; Spong, M.W., Advances in robot control, (2007), Springer Berlin, pp. 107-134
[26] Zhu, Y.H.; Qi, H.; Cheng, D., Synchronisation of a class of networked passive systems with switching topology, International journal of control, 82, 7, 1326-1333, (2009) · Zbl 1168.93395
[27] Hammel, D., Formation flight as an energy saving mechanism, Israel journal of zool, 41, 261-278, (1995)
[28] Andersson, M.; Wallander, J., Kin selection and reciprocity in flight formation, Behavioral ecology, 15, 1, 158-162, (2004)
[29] Liu, B.; Chu, T.; Wang, L.; Xie, G., Controllability of a leader – follower dynamic network with switching topology, IEEE transactions on automatic control, 53, 4, 1009-1013, (2008) · Zbl 1367.93074
[30] M. Ji, M. Egerstedt, A graph-theoretic characterization of controllability for multi-agent systems, in: Proceedings of the 2007 American Control Conference, New York, USA, 2007, pp. 4588-4593.
[31] Rahmani, A.; Ji, M.; Mesbahi, M.; Egerstedt, M., Controllability of multi-agent systems from a graph-theoretic perspective, SIAM journal on control and optimization, 48, 1, 162-186, (2009) · Zbl 1182.93025
[32] Cheng, D.; Wang, J.; Hu, X., An extension of lasall’s invariance principle and its application to multi-agent consensus, IEEE transactions on automatic control, 53, 7, 1765-1770, (2008) · Zbl 1367.93427
[33] Hong, Y.; Chen, G.; Bushnellc, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019
[34] Dimarogonasa, D.V.; Tsiotras, P.; Kyriakopoulos, K.J., Leader – follower cooperative attitude control of multiple rigid bodies, Systems & control letters, 58, 6, 429-435, (2009) · Zbl 1161.93002
[35] Consolini, L.; Morbidi, F.; Prattichizzo, D.; Tosques, M., Leader – follower formation control of nonholonomic mobile robots with input constraints, Automatica, 44, 5, 1343-1349, (2008) · Zbl 1283.93015
[36] Peng, K.; Yanga, Y., Leader-following consensus problem with a varying-velocity leader and time-varying delays, Physica A, 388, 2-3, 193-208, (2009)
[37] Wang, W.; Slotine, J.J.E., A theoretical study of different leader roles in networks, IEEE transactions on automatic control, 51, 7, 1156-1161, (2006) · Zbl 1366.93416
[38] Wang, J.; Cheng, D.; Hu, X., Consensus of multi-agent linear dynamical systems, Asian journal of control, 10, 2, 144-155, (2008)
[39] Wang, J.; Tan, Y.; Mareels, I., Robustness analysis of leader – follower consensus, Journal of systems science and complexity, 22, 2, 1559-7067, (2009)
[40] Wang, L.; Liu, Z., Robust consensus of multi-agent systems with noise, Science in China, series F, 52, 2, 824-834, (2009) · Zbl 1182.93011
[41] Horn, R.; Johnson, C., Matrix analysis, (1985), Cambridge University Press New York · Zbl 0576.15001
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