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**Consensus control for a class of networks of dynamic agents.**
*(English)*
Zbl 1266.93013

Summary: In this paper, the consensus problems for networks of dynamic agents are investigated. The agent dynamics is adopted as a typical point mass model based on the Newton’s law. The average-consensus problem is proposed for such class of networks, which includes two aspects, the agreement of the states of the agents and the convergence to zero of the speeds of the agents. A linear consensus protocol for such networks is established for solving such a consensus problem that includes two parts, a local speed feedback controller and the interactions from the finite neighbours. Two kinds of topology are discussed: one is fixed topology, the other is switching one. The convergence analysis is proved and the protocol performance is discussed as well. The simulation results are presented that are consistent with our theoretical results.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

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) |

### Keywords:

consensus control; algebraic graph theory; networks; distribute control; agents; fixed topology; switching topology
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\textit{G. Xie} and \textit{L. Wang}, Int. J. Robust Nonlinear Control 17, No. 10--11, 941--959 (2007; Zbl 1266.93013)

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### References:

[1] | Distributed Algorithms. Morgan Kaufmann: San Mateo, CA, 1997. |

[2] | Fax, IEEE Transactions on Automatic Control 49 pp 1465– (2004) |

[3] | On a dynamic extension of the theory of graphs. Proceedings of the American Control Conference 2002; Anchorage, AK, U.S.A., 1234–1239. |

[4] | Reynolds, Computer Graphics 21 pp 25– (1987) · Zbl 0942.68758 |

[5] | Gazi, IEEE Transactions on Automatic Control 48 pp 692– (2003) |

[6] | Gazi, IEEE Transactions on System Man and Cybernetics–B 34 pp 539– (2004) |

[7] | Liu, IEEE Transactions on Automatic Control 49 pp 30– (2004) |

[8] | Liu, IEEE Transactions on Automatic Control 48 pp 76– (2003) |

[9] | Liu, IEEE Transactions on Automatic Control 48 pp 1848– (2003) |

[10] | Vicsek, Physical Review Letters 75 pp 1226– (1995) |

[11] | Jadbabaie, IEEE Transactions on Automatic Control 48 pp 988– (2003) |

[12] | Savkin, IEEE Transactions on Automatic Control 49 pp 981– (2004) |

[13] | Olfati-Saber, IEEE Transactions on Automatic Control 49 pp 1520– (2004) |

[14] | . Consensus protocols for networks of dynamic agents. Proceedings of the American Control Conference, Denver, CO, U.S.A., 2003; 951–956. |

[15] | , . Stable flocking of mobile agents, part I: fixed topology. Proceedings of the IEEE Conference on Decision and Control, Hyatt Regency Maui, HI, U.S.A., vol. 2. 2003; 2010–2015. |

[16] | , . Stable flocking of mobile agents, part II: dynamic topology. Proceedings of the IEEE Conference on Decision and Control, Hyatt Regency Maui, HI, U.S.A., vol. 2. 2003; 2016–2021. |

[17] | , . Swarming behavior of multi-agent systems. Proceedings of the 23rd Chinese Control Conference, Wuxi, China, August 2004; 1027–1031. |

[18] | , , . Coordination of a group of mobile autonomous agents. International Conference on Advances in intelligent Systems–Theory and Applications, Luxembourg, November 2004. |

[19] | , , , . Aggregation of Forging Swarms. Lecture Notes in Artificial Intelligence, vol. 3339, 2004; 766–777. |

[20] | Liu, Chinese Physics Letters 22 pp 254– (2005) |

[21] | , . Collective motion in a group of mobile autonomous agents. IEEE International Conference on Advance in Intelligent Systems–Theory and Applications, Luxembourg, November 2004. |

[22] | Mesbahi, AIAA Journal of Guidance Control and Dynamics 24 pp 369– (2000) |

[23] | Desai, IEEE Transactions on Robotics and Automation 17 pp 905– (2001) |

[24] | Lawton, IEEE Transactions on Robotics and Automation 19 pp 933– (2003) |

[25] | . Consensus of information under dynamically changing interaction topologies. Proceedings of the American Control Conference, Boston, MA, U.S.A., 2004; 4939–4944. |

[26] | , . Graph theoretic methods in the stability of vehicle formations. Proceedings of the American Control Conference, Boston, MA, U.S.A., 2004; 3729–3734. |

[27] | Lafferriere, Systems and Control Letters 54 pp 899– (2005) |

[28] | Ren, IEEE Transactions on Automatic Control 1 pp 655– (2005) |

[29] | Strogatz, Nature 410 pp 268– (2001) |

[30] | , . Chemical Oscillators, Waves, and Turbulance. Springer: Berlin, Germany, 1984. |

[31] | Acebron, Physical Review Letters 81 pp 2229– (1998) |

[32] | Toner, Physical Review E 58 pp 4828– (1998) |

[33] | Levine, Physical Review E 63 pp 017101-1– (2001) |

[34] | Rosenblum, Physical Review Letters 92 pp 114102-1– (2004) |

[35] | Kiss, Physical Review E 70 pp 026210-1– (2004) |

[36] | Scire, Physical Review E 70 pp 035201-1– (2004) |

[37] | Woafo, Physical Review E 69 pp 046206-1– (2004) |

[38] | Rosenblum, Physical Review Letters 92 pp 114102-1– (2004) |

[39] | Algebraic Graph Theory. Cambridge University Press: Cambridge, U.K., 1974. · Zbl 0797.05032 |

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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.