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**Tracking control for multi-agent consensus with an active leader and variable topology.**
*(English)*
Zbl 1117.93300

Summary: We consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.

### MSC:

93A13 | Hierarchical systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93B52 | Feedback control |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{Y. Hong} et al., Automatica 42, No. 7, 1177--1182 (2006; Zbl 1117.93300)

### References:

[1] | Fax, A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1453-1464, (2004) |

[2] | Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer New York · Zbl 0968.05002 |

[3] | Horn, R.; Johnson, C., Matrix analysis, (1985), Cambridge University Press New York · Zbl 0576.15001 |

[4] | Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 998-1001, (2003) · Zbl 1364.93514 |

[5] | Lin, Z.; Broucke, M.; Francis, B., Local control strategies for groups of mobile autonomous agents, IEEE transactions on automatic control, 49, 4, 622-629, (2004) · Zbl 1365.93208 |

[6] | Merris, R., Laplacian matrices of graphs: A survey, Linear algebra and applications, 197, 143-176, (1994) · Zbl 0802.05053 |

[7] | Olfati-Saber, R.; Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 |

[8] | Savkin, A., Coordinated collective motion of groups of autonomous mobile robots: analysis of Vicsek’s model, IEEE transactions on automatic control, 49, 6, 981-983, (2004) · Zbl 1365.93327 |

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