Containment control of multiagent systems with multiple leaders and noisy measurements.

*(English)*Zbl 1242.93093Summary: We consider the distributed containment control of multiagent systems with multiple stationary leaders and noisy measurements. A stochastic approximation type and consensus-like algorithm is proposed to solve the containment control problem. We provide conditions under which all the followers can converge both almost surely and in mean square to the stationary convex hull spanned by the leaders. Simulation results are provided to illustrate the theoretical results.

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\textit{Z.-J. Tang} et al., Abstr. Appl. Anal. 2012, Article ID 262153, 9 p. (2012; Zbl 1242.93093)

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[1] | R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, 2004. · Zbl 1365.93301 · doi:10.1109/TAC.2004.834113 |

[2] | P. Lin and Y. Jia, “Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies,” IEEE Transactions on Automatic Control, vol. 55, no. 3, pp. 778-784, 2010. · Zbl 1368.93275 · doi:10.1109/TAC.2010.2040500 |

[3] | Y. G. Sun and L. Wang, “Consensus of multi-agent systems in directed networks with uniform time-varying delays,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1607-1613, 2009. · Zbl 1367.93574 · doi:10.1109/TAC.2009.2017963 |

[4] | M. Huang and J. H. Manton, “Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 134-161, 2009. · Zbl 1182.93108 · doi:10.1137/06067359X |

[5] | T. Li and J.-F. Zhang, “Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2043-2057, 2010. · Zbl 1368.93548 · doi:10.1109/TAC.2010.2042982 |

[6] | J. Hu and G. Feng, “Distributed tracking control of leader-follower multi-agent systems under noisy measurement,” Automatica, vol. 46, no. 8, pp. 1382-1387, 2010. · Zbl 1204.93011 · doi:10.1016/j.automatica.2010.05.020 |

[7] | L. Moreau, “Stability of multiagent systems with time-dependent communication links,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 169-182, 2005. · Zbl 1365.93268 · doi:10.1109/TAC.2004.841888 |

[8] | W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655-661, 2005. · Zbl 1365.93302 · doi:10.1109/TAC.2005.846556 |

[9] | D. Cheng, J. Wang, and X. Hu, “An extension of LaSalle’s invariance principle and its application to multi-agent consensus,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1765-1770, 2008. · Zbl 1367.93427 · doi:10.1109/TAC.2008.928332 |

[10] | M. Porfiri and D. J. Stilwell, “Consensus seeking over random weighted directed graphs,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1767-1773, 2007. · Zbl 1366.93330 · doi:10.1109/TAC.2007.904603 |

[11] | B. Liu and T. Chen, “Consensus in networks of multiagents with cooperation and competition via stochastically switching topologies,” IEEE Transactions on Neural Networks, vol. 19, no. 11, pp. 1967-1973, 2008. |

[12] | J. CortĂ©s, “Finite-time convergent gradient flows with applications to network consensus,” Automatica, vol. 42, no. 11, pp. 1993-2000, 2006. · Zbl 1261.93058 · doi:10.1016/j.automatica.2006.06.015 |

[13] | L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950-955, 2010. · Zbl 1368.93391 · doi:10.1109/TAC.2010.2041610 |

[14] | A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, 2003. · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781 |

[15] | Y. Hong, L. Gao, D. Cheng, and J. Hu, “Lyapunov-based approach to multiagent systems with switching jointly connected interconnection,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 943-948, 2007. · Zbl 1366.93437 · doi:10.1109/TAC.2007.895860 |

[16] | Y. Hong, J. Hu, and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177-1182, 2006. · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013 |

[17] | W. Ren, “Multi-vehicle consensus with a time-varying reference state,” Systems & Control Letters, vol. 56, no. 7-8, pp. 474-483, 2007. · Zbl 1157.90459 · doi:10.1016/j.sysconle.2007.01.002 |

[18] | W. Ren, “Consensus tracking under directed interaction topologies: algorithms and experiments,” IEEE Transactions on Control Systems Technology, vol. 18, no. 1, pp. 230-237, 2010. |

[19] | J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with cou-pling time delays,” Physica A, vol. 374, no. 2, pp. 853-863, 2007. |

[20] | W. Zhu and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994-1999, 2010. · Zbl 1205.93056 · doi:10.1016/j.automatica.2010.08.003 |

[21] | M. Ji, G. Ferrari-Trecate, M. Egerstedt, and A. Buffa, “Containment control in mobile networks,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1972-1975, 2008. · Zbl 1367.93398 · doi:10.1109/TAC.2008.930098 |

[22] | G. Notarstefano, M. Egerstedt, and M. Haque, “Containment in leader-follower networks with switching communication topologies,” Automatica, vol. 47, no. 5, pp. 1035-1040, 2011. · Zbl 1233.93009 · doi:10.1016/j.automatica.2011.01.077 |

[23] | Y. Cao and W. Ren, “Containment control with multiple stationary or dynamic lead-ers under a directed interaction graph,” in Proceedings of the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, pp. 3014-3019, IEEE, Shanghai, China, 2009. |

[24] | Z. Li, W. Ren, X. Liu, and M. Fu, “Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders,” International Journal of Robust and Nonlinear Control. In press. · Zbl 1284.93019 · doi:10.1002/rnc.1847 |

[25] | M. Huang and J. H. Manton, “Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies,” IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 235-241, 2010. · Zbl 1368.94002 · doi:10.1109/TAC.2009.2036291 |

[26] | H. Chen, Stochastic Approximation and Its Application, Kluwer, Boston, Mass, USA, 2002. · Zbl 1008.62071 |

[27] | R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, NY, USA, 1994. · Zbl 0801.15001 |

[28] | T.-Z. Huang and Y. Zhu, “Estimation of \parallel A-1\parallel \infty for weakly chained diagonally dominant M-matrices,” Linear Algebra and its Applications, vol. 432, no. 2-3, pp. 670-677, 2010. · Zbl 1181.15024 · doi:10.1016/j.laa.2009.09.012 |

[29] | P. N. Shivakumar, J. J. Williams, Q. Ye, and C. A. Marinov, “On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital circuit dynamics,” SIAM Journal on Matrix Analysis and Applications, vol. 17, no. 2, pp. 298-312, 1996. · Zbl 0853.15013 · doi:10.1137/S0895479894276370 |

[30] | B. T. Polyak, Introduction to Optimization, Optimization Software, New York, NY, USA, 1987. · Zbl 0708.90083 |

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