Group consensus in multi-agent systems with switching topologies and communication delays.

*(English)*Zbl 1197.93096Summary: Group consensus problems in networks of dynamic agents are addressed for two cases: (i) communication topologies are switching and the switching occurs among finite topologies arbitrarily; (ii) communication topologies are switching and the switching occurs among finite topologies arbitrarily, and there exist communication delays. We introduce double-tree-form transformations under which dynamic equations of agents are transformed into reduced-order systems. Based on the reduced-order systems, we obtain some analysis results for the two cases. In addition, we further investigate multi-group consensus as an extension of the group consensus, and present some analysis results by similar techniques. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

##### MSC:

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

93A14 | Decentralized systems |

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\textit{J. Yu} and \textit{L. Wang}, Syst. Control Lett. 59, No. 6, 340--348 (2010; Zbl 1197.93096)

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##### References:

[1] | R.W. Beard, V. Stepanyan, Synchronization of information in distributed multiple vehicle coordination control, in: Proc. IEEE Conf. Decision and Control, Maui, HI, Dec. 2003, pp. 2029-2034. |

[2] | Xiao, L.; Boyd, S., Fast linear iterations for distributed averaging, Systems control lett., 53, 65-78, (2004) · Zbl 1157.90347 |

[3] | T. Chu, L. Wang, T. Chen, Self-organized motion in a class of anisotropic swarms, in: Proc. Amer. Control Conf., Portland, OR, USA, June 2005, pp. 3474-3479. |

[4] | Vicsek, T.; Czirok, A.; Jacob, E.B.; Cohen, I.; Schochet, O., Novel type of phase transitions in a system of self-driven particles, Phys. rev. lett., 75, 1226-1229, (1995) |

[5] | F. Xiao, L. Wang, Reaching agreement in finite time via continuous local state feedback, in: Proc. 26th Chinese Control Conf., 2007, pp. 711-715. |

[6] | Cao, M.; Morse, A.S.; Anderson, B.D.O., Agreeing asynchronously, IEEE trans. automat. control, 53, 8, 1826-1838, (2008) · Zbl 1367.93359 |

[7] | Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE trans. automat. control, 48, 6, 988-1001, (2003) · Zbl 1364.93514 |

[8] | 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 |

[9] | 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 |

[10] | Xiao, F.; Wang, L., Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44, 10, 2577-2582, (2008) · Zbl 1155.93312 |

[11] | 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 |

[12] | Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, Int. J. robust & nonlin. control, 17, 10-11, 1002-1033, (2007) · Zbl 1266.93010 |

[13] | Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE trans. automat. control, 50, 169-182, (2005) · Zbl 1365.93268 |

[14] | Sun, Y.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems control lett., 57, 2, 175-183, (2008) · Zbl 1133.68412 |

[15] | Xiao, F.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE trans. automat. control, 53, 8, 1804-1816, (2008) · Zbl 1367.93255 |

[16] | Porfiri, M.; Stilwell, D.J., Consensus seeking over random weighted directed graphs, IEEE trans. automat. control, 52, 9, 1767-1773, (2007) · Zbl 1366.93330 |

[17] | Tahbaz-Salehi, A.; Jadbabaie, A., A necessary and sufficient condition for consensus over random networks, IEEE trans. automat. control, 53, 3, 791-795, (2008) · Zbl 1367.90015 |

[18] | Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138 |

[19] | W. Ren, R.W. Beard, E.M. Atkins, A survey of consensus problems in multi-agent coordination, in: Proc. Amer. Control Conf., Portland, 2005, pp. 1859-1864. |

[20] | Sun, Y.; 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 |

[21] | J. Yu, L. Wang, Group consensus in multi-agent systems with undirected communication graphs, in: Proc. 7th Asian Control Conf., 2009, pp. 105-110. |

[22] | Xiao, F.; Wang, L., Consensus problems for high-dimensional multi-agent systems, IET control theory appl., 1, 3, 830-837, (2007) |

[23] | Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE trans. automat. control, 43, 475-482, (1998) · Zbl 0904.93036 |

[24] | Liberzon, D.; Morse, A.S., Basic problems in stability and design of switched systems, IEEE control mag., 19, 59-70, (1999) · Zbl 1384.93064 |

[25] | Lin, H.; Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results, IEEE trans. automat. control, 54, 2, 308-322, (2009) · Zbl 1367.93440 |

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