Second-order consensus for multi-agent systems with switching topology and communication delay. (English) Zbl 1225.93020
Summary: Two kinds of consensus problems for second-order agents under directed and arbitrarily switching topologies are investigated, that is, the cases without and with communication delay. For the former, by constructing a new kind of digraph and employing a new graphic method, we can specify the least convergence rate for all the agents to reach consensus. For the latter, in virtue of a matrix inequality method, a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus. This, on the other hand, shows that consensus can be reached if the delay is small enough. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.
MSC:
| 93A14 | Decentralized systems |
| 94C15 | Applications of graph theory to circuits and networks |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
References:
| [1] | 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., 47, 2, 601-623 (2008) · Zbl 1157.93434 |
| [2] | Jadbabaie, A.; Lin, J.; Morse, S. A., Coordination of groups of mobile agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 |
| [3] | Ji, Z.; Wang, Z.; Lin, H.; Wang, Z., Controllability of multi-agent systems with time-delay in state and switching topology, Internat. J. Control, 83, 2, 371-386 (2010) · Zbl 1184.93017 |
| [4] | Ji, Z.; Wang, Z.; Lin, H.; Wang, Z., Interconnection topologies for multi-agent coordination under leader-follower framework, Automatica, 45, 12, 2857-2863 (2009) · Zbl 1192.93013 |
| [5] | Lin, P.; Jia, Y., Average consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A, 387, 1, 303-313 (2008) |
| [6] | Lan, Y.; Yan, G.; Lin, Z., Distributed control of cooperative target enclosing based on reachability and invariance analysis, Syst. Control Lett., 59, 7, 381-389 (2010) · Zbl 1200.93105 |
| [7] | Hatano, Y.; Mesbahi, M., Agreement over random networks, IEEE Trans. Automat. Control, 50, 11, 1867-1872 (2005) · Zbl 1365.94482 |
| [8] | Ren, W., Multi-vehicle consensus with a time-varying reference state, Syst. Control Lett., 56, 7-8, 474-483 (2007) · Zbl 1157.90459 |
| [9] | Olfati-saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301 |
| [10] | Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 |
| [11] | Sun, Y. G.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Syst. Control Lett., 57, 2, 175-183 (2008) · Zbl 1133.68412 |
| [12] | Sun, Y. G.; Wang, L., Consensus of multi-agent systems in directed networks with nonuniform time-varying delays, IEEE Trans. Automat. Control, 54, 7, 1607-1613 (2009) · Zbl 1367.93574 |
| [13] | Xiao, F.; Wang, L., State consensus for multi-agent systems with switching topologies and time-varying delays, Internat. J. Control, 79, 10, 1277-1284 (2006) · Zbl 1330.94022 |
| [14] | Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Trans. Automat. Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056 |
| [15] | Olfati-saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Trans. Automat. Control, 51, 3, 401-420 (2006) · Zbl 1366.93391 |
| [16] | J. Qin, W.X. Zheng, H. Gao, Sampled-data consensus for multiple agents with discrete second-order dynamics, in: Proc. 49th IEEE Conf. Decision Control, Atlanta, GA, USA, 2010, pp. 1391-1396.; J. Qin, W.X. Zheng, H. Gao, Sampled-data consensus for multiple agents with discrete second-order dynamics, in: Proc. 49th IEEE Conf. Decision Control, Atlanta, GA, USA, 2010, pp. 1391-1396. |
| [17] | Peng, K.; Yang, Y., Leader-following consensus problem with a varying-velocity leader and time-varying delays, Physica A, 388, 2-3, 193-208 (2009) |
| [18] | Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Trans. Automat. Control, 53, 6, 1503-1509 (2008) · Zbl 1367.93567 |
| [19] | Ren, W.; Atkins, E. M., Distributed multi-vehicle coordinated control via local information exchange, Internat. J. Robust Nonlinear Control, 17, 10-11, 1002-1033 (2007) · Zbl 1266.93010 |
| [20] | Tanner, H. G.; Jadbabaie, A.; Pappas, G. J., Flocking in fixed and switching networks, IEEE Trans. Automat. Control, 52, 5, 863-868 (2007) · Zbl 1366.93414 |
| [21] | Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents, Internat. J. Robust Nonlinear Control, 17, 10-11, 941-959 (2007) · Zbl 1266.93013 |
| [22] | Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019 |
| [23] | Yu, W.; Chen, G.; Cao, M., Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities, Syst. Control Lett., 59, 9, 543-552 (2010) · Zbl 1207.37054 |
| [24] | Zhu, J.; Tian, Y.; Kuang, J., On the general consensus protocol of multi-agent systems with double-integrator dynamics, Linear Algebra Appl., 431, 5-7, 701-715 (2009) · Zbl 1165.93022 |
| [25] | Godsil, C.; Doyle, G., Algebraic Graph Theory (2001), Springer: Springer New York · Zbl 0968.05002 |
| [26] | P. Lin, Y. Jia, J. Du, F. Yu, Distributed leadless coordination for networks of second-order agents with time-delay on switching topology, in: Proc. 2008 Amer. Control Conf., Seattle, WA, USA, 2008, pp. 1564-1569.; P. Lin, Y. Jia, J. Du, F. Yu, Distributed leadless coordination for networks of second-order agents with time-delay on switching topology, in: Proc. 2008 Amer. Control Conf., Seattle, WA, USA, 2008, pp. 1564-1569. |
| [27] | Qin, J.; Gao, H.; Zheng, W. X., On average consensus in directed networks of agents with switching topology and time-delay, Internat. J. Systems Sci. (2010) |
| [28] | F. Gouaisbaut, D. Peaucelle, A note on stability of time delay systems, in: Proc. 5th IFAC Symp. Robust Control Design, Toulouse, France, 2006.; F. Gouaisbaut, D. Peaucelle, A note on stability of time delay systems, in: Proc. 5th IFAC Symp. Robust Control Design, Toulouse, France, 2006. · Zbl 1293.93589 |
| [29] | Gu, K.; Kharitonov, V. L.; Chen, J., Stability of Time-Delay Systems (2003), Springer-Verlag: Springer-Verlag Berlin, Germany · Zbl 1039.34067 |
| [30] | Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004 |
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