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**Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity.**
*(English)*
Zbl 1270.93004

Summary: This paper is concerned with the second-order consensus problem of multi-agent systems with a virtual leader, where all agents and the virtual leader share the same intrinsic dynamics with a locally Lipschitz condition. It is assumed that only a small fraction of agents in the group are informed about the position and velocity of the virtual leader. A connectivity-preserving adaptive controller is proposed to ensure the consensus of multi-agent systems, wherein no information about the nonlinear dynamics is needed. Moreover, it is proved that the consensus can be reached globally with the proposed control strategy if the degree of the nonlinear dynamics is smaller than some analytical value. Numerical simulations are further provided to illustrate the theoretical results.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93C40 | Adaptive control/observation systems |

### Keywords:

adaptive consensus; Lipschitz condition; multi-agent systems; nonlinearity; second-order consensus; virtual leader
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\textit{Y. Hu} et al., Int. J. Robust Nonlinear Control 23, No. 9, 978--990 (2013; Zbl 1270.93004)

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### References:

[1] | Fax, Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control 49 (9) pp 1465– (2004) · Zbl 1365.90056 |

[2] | Olfati-Saber, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95 (1) pp 215– (2007) · Zbl 1376.68138 |

[3] | Cao, Reaching a consensus in a dynamically changing environment: convergence rates, measurement delays, and asynchronous events, SIAM Journal on Control and Optimization 47 (2) pp 601– (2008) · Zbl 1157.93434 |

[4] | Olfati-Saber, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control 49 (9) pp 1520– (2004) · Zbl 1365.93301 |

[5] | Su, Synchronization of coupled harmonic oscillators in a dynamic proximity network, Automatica 45 (10) pp 2286– (2009) · Zbl 1179.93102 |

[6] | Su, Second-order consensus of multiple agents with coupling delay, Communications in Theoretical Physics 51 (1) pp 101– (2009) · Zbl 1172.93305 |

[7] | Su, Flocking in multi-agent systems with multiple virtual leaders, Asian Journal of Control 10 (2) pp 238– (2008) |

[8] | Ren, Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications (2008) · Zbl 1144.93002 |

[9] | Lafferriere, Decentralized control of vehicle formations, Systems & Control Letters 54 (9) pp 899– (2005) · Zbl 1129.93303 |

[10] | Ren, On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control 53 (6) pp 1503– (2008) · Zbl 1367.93567 |

[11] | Ren, Distributed multi-vehicle coordinated control via local information exchange, International Journal of Robust and Nonlinear Control 17 (10-11) pp 1002– (2007) · Zbl 1266.93010 |

[12] | Su, Adaptive second-order consensus of networked mobile agents with nonlinear dynamics, Automatica 47 (2) pp 368– (2011) · Zbl 1207.93006 |

[13] | Su, Flocking of multi-agents with a virtual leader, IEEE Transactions on Automatic Control 54 (2) pp 293– (2009) · Zbl 1367.37059 |

[14] | Ren, Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE Control Systems Magazine 27 (2) pp 71– (2007) |

[15] | Wu, Synchronization in Coupled Chaotic Circuits and Systems (2002) · Zbl 1007.34044 |

[16] | Wang, Pinning control of scale-free dynamical networks, Physica A 310 (3-4) pp 521– (2002) · Zbl 0995.90008 |

[17] | Das, Distributed adaptive control for synchronization of unknown nonlinear networked systems, Automatica 46 (12) pp 2014– (2010) · Zbl 1205.93045 |

[18] | Wu, Synchronization in Complex Networks of Nonlinear Dynamical Systems (2007) · Zbl 1135.34002 |

[19] | Hou, Decentralized robust adaptive control for the multiagent system consensus problem using neural networks, IEEE Transactions on Systems, Man and Cybernetics - Part B 39 (3) pp 636– (2009) |

[20] | Cheng, Neural-network based adaptive leader-following control for multi-agent systems with uncertainties, IEEE Transactions on Neural Networks 21 (8) pp 1351– (2010) |

[21] | Yu, Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Transactions on Systems, Man and Cybernetics - Part B 40 (3) pp 881– (2010) |

[22] | Lü, Bridge the gap between the Lorenz system and the Chen system, International Journal of Bifurcation and Chaos 12 (12) pp 2917– (2002) · Zbl 1043.37026 |

[23] | Rinzel, Dissection of a model for neuronal parabolic bursting, Journal of Mathematical Biology 25 (6) pp 653– (1987) · Zbl 0628.92016 |

[24] | Rössler, An equation for continuous chaos, Physics Letters A 57 (5) pp 397– (1976) · Zbl 1371.37062 |

[25] | Vano, Chaos in low-dimensional Lotka-Volterra models of competition, Nonlinearity 19 pp 2391– (2006) · Zbl 1107.92058 |

[26] | Su, A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements, International Journal of Control 82 (7) pp 1334– (2009) · Zbl 1168.93311 |

[27] | Su, Rendezvous of multiple mobile agents with preserved network connectivity, Systems and Control Letters 59 (5) pp 313– (2010) · Zbl 1191.93005 |

[28] | Hong, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42 (7) pp 1177– (2006) · Zbl 1117.93300 |

[29] | Khalil, Nonlinear Systems (2002) |

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.