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Reaching a consensus via pinning control. (English) Zbl 1162.93305
Summary: The consensus problem in a multi-agent system with general nonlinear coupling is investigated in this paper. It is demonstrated that, under suitable conditions on communication, all agents approach a prescribed value if a small fraction of them are controlled by simple feedback control. The stability analysis is based on a blend of graph-theoretic and system-theoretic tools where the contraction analysis and multiple Lyapunov functions play central roles. Numerous numerical examples, which support the analytical results very well, are also included.

93A14Decentralized systems
93B52Feedback control
93C85Automated control systems (robots, etc.)
93D30Scalar and vector Lyapunov functions
Full Text: DOI
[1] Branicky, M. S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE transaction on automatic control 43, No. 4, 475-482 (1998) · Zbl 0904.93036 · doi:10.1109/9.664150
[2] Grigoriev, R. O.; Cross, M. C.; Schuster, H. G.: Pinning control of spatiotemporal chaos, Physical review letters 79, No. 15, 2795-2798 (1997)
[3] Hong, Y. G.; Gao, L. X.; Cheng, D. Z.; Hu, J. P.: Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE transaction on automatic control 52, No. 5, 943-948 (2007)
[4] Hong, Y. G.; Hu, J. P.; Gao, L. X.: Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42, 1177-1182 (2006) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013
[5] Jadbabaie, A.; Lin, J.; Morse, A. S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transaction on automatic control 48, No. 6, 988-1001 (2003)
[6] Jin, Z.; Murray, R. M.: Cooperative networks, control and optimization, , 31-47 (2008)
[7] Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002
[8] Li, X.; Wang, X. F.; Chen, G. R.: Pinning a complex dynamical network to its equilibrium, IEEE transactions on circuits and systems-I: regular papers 51, No. 10, 2074-2087 (2004)
[9] Lohmiller, W., & Slotine, J. J. E. (1996). On metric observers for nonlinear systems. In IEEE int. conf. on control applications (pp. 320-326)
[10] Moore, K., & Lucarelli, D. (2005). Forced and constrained consensus among cooperating agents. In IEEE international conference on networking, sensing and control (pp. 449-454)
[11] Moreau, L.: Stability of multiagent systems with time-dependent communication links, IEEE transaction on automatic control 50, No. 2, 169-182 (2005)
[12] Olfati-Saber, R.: Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95, No. 1, 215-233 (2007)
[13] Ren, W.: Multi-vehicle consensus with a time-varying reference state, Systems & control letters 56, 474-483 (2007) · Zbl 1157.90459 · doi:10.1016/j.sysconle.2007.01.002
[14] Ren, W., Beard, R. W., & Atkins, E. M. (2005). A survey of consensus problems in multi-agent coordination. In Proceeding of 2005 American Control Conference (pp. 1859-1864)
[15] Tanner, H. G. (2004). On the controllability of nearest neighbor interconnections. In IEEE conference on decision and control (pp. 2467-2472)
[16] Xiang, J.; Chen, G. R.: On the v-stability of complex dynamical networks, Automatica 43, 1049-1057 (2006) · Zbl 05246818
[17] Zhou, J.; Lu, J. A.; Lü, J. H.: Adaptive synchronization of an uncertain complex dynamical network, IEEE transaction on automatic control 51, No. 4, 652-656 (2006)
[18] Zhou, J.; Lu, J. A.; Lü, J. H.: Pinning adaptive synchronization of a general complex dynamical network, Automatica 44, 996-1003 (2008) · Zbl 1283.93032