##
**Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements.**
*(English)*
Zbl 1252.93009

Summary: This paper studies the finite-time consensus problem of heterogeneous multi-agent systems composed of first-order and second-order integrator agents. By combining the homogeneous domination method with the adding a power integrator method, we propose two classes of consensus protocols with and without velocity measurements. First, we consider the protocol with velocity measurements and prove that it can solve the finite-time consensus under a strongly connected graph and leader-following network, respectively. Second, we consider the finite-time consensus problem of heterogeneous multi-agent systems, for which the second-order integrator agents cannot obtain the velocity measurements for feedback. Finally, some examples are provided to illustrate the effectiveness of the theoretical results.

### MSC:

93A14 | Decentralized systems |

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

### Keywords:

heterogeneous multi-agent systems; finite-time consensus; velocity measurements; graph theory
PDFBibTeX
XMLCite

\textit{Y. Zheng} and \textit{L. Wang}, Syst. Control Lett. 61, No. 8, 871--878 (2012; Zbl 1252.93009)

Full Text:
DOI

### References:

[1] | Chu, T.; Wang, L.; Chen, T.; Mu, S., Complex emergent dynamics of anisotropic swarms: convergence vs. oscillation, Chaos, Solitons and Fractals, 30, 4, 875-885 (2006) · Zbl 1142.34346 |

[2] | 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 |

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

[4] | 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 |

[5] | Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 |

[6] | Kim, Y.; Mesbahi, M., On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian, IEEE Transactions on Automatic Control, 51, 1, 116-120 (2006) · Zbl 1366.05069 |

[7] | Xiao, L.; Boyd, S., Fast linear iterations for distributed averaging, Systems and Control Letters, 53, 1, 65-78 (2004) · Zbl 1157.90347 |

[8] | Cortés, J., Finite-time convergent gradient flows with applications to network consensus, Automatica, 42, 11, 1993-2000 (2006) · Zbl 1261.93058 |

[9] | Hui, Q., Finite-time rendezvous algorithms for mobile autonomous agent, IEEE Transactions on Automatic Control, 56, 1, 207-211 (2011) · Zbl 1368.93375 |

[10] | Chen, G.; Lewis, F. L.; Xie, L., Finite-time distributed consensus via binary control protocols, Automatica, 47, 9, 1962-1968 (2011) · Zbl 1226.93008 |

[11] | Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuos autonomous systems, SIAM Journal on Control and Optimization, 38, 3, 751-766 (2000) · Zbl 0945.34039 |

[12] | Wang, L.; Xiao, F., Finite-time consensus problems for networks of dynamic agents, IEEE Transactions on Automatic Control, 55, 4, 950-955 (2010) · Zbl 1368.93391 |

[13] | F. Xiao, Consensus problems in networks of multiple autonomous agents, Ph.D. Thesis, Peking University, Beijing, China, 2008.; F. Xiao, Consensus problems in networks of multiple autonomous agents, Ph.D. Thesis, Peking University, Beijing, China, 2008. |

[14] | Jiang, F.; Wang, L., Finite-time information consensus for multi-agent systems with fixed and switching topologies, Physica D, 238, 16, 1550-1560 (2009) · Zbl 1170.93304 |

[15] | Jiang, F.; Wang, L., Finite-time weighted average consensus with respect to a monotinic function and its application, Systems and Control Letters, 60, 9, 718-725 (2011) · Zbl 1226.93012 |

[16] | Zheng, Y.; Chen, W.; Wang, L., Finite-time consensus for stochastic multi-agent systems, International Journal of Control, 84, 10, 1644-1652 (2011) · Zbl 1236.93141 |

[17] | X. Wang, Y. Hong, Finite-time consensus for multi-agent networks with second-order agent dynamics, in: Proceedings of the 17th World Congress The International Federation of Automatic Control, Seoul, Korea, July 6-11, 2008, pp. 15185-15190.; X. Wang, Y. Hong, Finite-time consensus for multi-agent networks with second-order agent dynamics, in: Proceedings of the 17th World Congress The International Federation of Automatic Control, Seoul, Korea, July 6-11, 2008, pp. 15185-15190. |

[18] | Li, S.; Du, H.; Lin, X., Finite-time consensus for multi-agent systems with double-integrator dynamics, Automatica, 47, 8, 1706-1712 (2011) · Zbl 1226.93014 |

[19] | Qian, C.; Li, J., Global finite-time stabilization by output feedback for plannar systems without observable linearization, IEEE Transactions on Automatic Control, 50, 6, 885-890 (2005) · Zbl 1365.93415 |

[20] | Liu, C.; Liu, F., Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica, 47, 9, 2130-2133 (2011) · Zbl 1227.93010 |

[21] | Zheng, Y.; Zhu, Y.; Wang, L., Consensus of heterogeneous multi-agent systems, IET Control Theory and Applications, 5, 16, 1881-1888 (2011) |

[22] | Zheng, Y.; Wang, L., Consensus of heterogeneous multi-agent systems without velocity measrements, International Journal of Control, 85, 7, 906-914 (2012) · Zbl 1282.93031 |

[23] | Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control, 53, 6, 1503-1509 (2008) · Zbl 1367.93567 |

[24] | Y. Gao, L. Wang, Y. Jia, Consensus of multiple second-order agents without velocity measurements, in: Proceedings of the American Control Conference, St. Louis, USA, June 10-12, 2009, pp. 4464-4469.; Y. Gao, L. Wang, Y. Jia, Consensus of multiple second-order agents without velocity measurements, in: Proceedings of the American Control Conference, St. Louis, USA, June 10-12, 2009, pp. 4464-4469. |

[25] | Abdessameud, A.; Tayebi, A., On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints, Systems and Control Letters, 59, 12, 812-821 (2010) · Zbl 1217.93009 |

[26] | Godsil, C.; Royal, G., Algebraic Graph Theory (2001), Springer-Verlag: Springer-Verlag New York · Zbl 0968.05002 |

[27] | Hong, Y., Finite-time stabilization and stabilizability of a class of controllable systems, Systems and Control Letters, 46, 4, 231-236 (2002) · Zbl 0994.93049 |

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.