Distributed tracking control of leader-follower multi-agent systems under noisy measurement.

*(English)*Zbl 1204.93011Summary: A distributed tracking control scheme with distributed estimators has been developed for a leader-follower multi-agent system with measurement noises and directed interconnection topology. It is supposed that each follower can only measure the relative positions of its neighbors in a noisy environment, including the relative position of the second-order active leader. A neighbor-based tracking protocol together with distributed estimators is designed based on a novel velocity decomposition technique. It is shown that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well. A simulation example is finally given to illustrate the performance of the proposed control scheme.

##### MSC:

93A14 | Decentralized systems |

93E15 | Stochastic stability in control theory |

93E10 | Estimation and detection in stochastic control theory |

94C15 | Applications of graph theory to circuits and networks |

##### Keywords:

multi-agent systems; leader-follower; velocity decomposition; state estimation; stochastic noises##### References:

[1] | Anderson, B.D.O.; Fidan, B.; Yu, C.; Walle, D., UAV formation control: theory and application, (), 15-33 · Zbl 1201.93089 |

[2] | Chow, Y.S.; Teicher, H., Probability theory: independence, interchangeability, martingales, (1997), Springer New York · Zbl 0891.60002 |

[3] | Das, A.K.; Fierro, R.; Kumar, V., A vision-based formation control framework, IEEE robotics and automation society, 18, 5, 813-825, (2002) |

[4] | Fax, A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056 |

[5] | Friedman, A., Stochastic differential equations and applications: vol. 1, (1975), Academic Press New York · Zbl 0323.60056 |

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

[7] | Gupta, H., Cao, X., & Haering, N. (2008). Map-based active leader – follower surveillance system. In Proc. of ECCV workshop on multi-camera and multi-modal sensor fusion algorithms and applications, Marseille, France. |

[8] | Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182, (2006) · Zbl 1117.93300 |

[9] | Hu, J.; Hong, Y., Leader-following coordination of multi-agent systems with coupling time delays, Physica A, 374, 2, 853-863, (2007) |

[10] | Hu, J.; Hu, X., Optimal target trajectory estimation and filtering using networked sensors, Journal of systems science & complexity, 21, 325-336, (2008) · Zbl 1173.93377 |

[11] | Huang, M.; Manton, J.H., Coordination and consensus of networked agents with noisy measurement: stochastic algorithms and asymptotic behavior, SIAM journal on control and optimization, 48, 1, 134-161, (2009) · Zbl 1182.93108 |

[12] | 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, 988-1001, (2003) · Zbl 1364.93514 |

[13] | Lin, Z.; Francis, B.; Maggiore, M., Necessary and sufficient graphical conditions for formation control of unicycles, IEEE transactions on automatic control, 50, 1, 121-127, (2005) · Zbl 1365.93324 |

[14] | Lin, P.; Jia, Y.; Du, J.; Yuan, S., Distributed control of multi-agent systems with second-order agent dynamics and delay-dependent communications, Asian journal of control, 10, 2, 254-259, (2008) |

[15] | Li, T.; Zhang, J.F., Mean square average consensus under measurement noises and fixed topologies: necessary and sufficient conditions, Automatica, 45, 8, 1929-1936, (2009) · Zbl 1185.93006 |

[16] | Michel, A.N.; Miller, R.K., Qualitative analysis of large scale dynamical systems, (1977), Academic Press New York · Zbl 0358.93028 |

[17] | Nevelson, M.B.; Hasminskii, R.Z., Stochastic approximation and recursive estimation, (1976), American Mathematical Society Providence |

[18] | 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 |

[19] | Shi, G.; Hong, Y., Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies, Automatica, 45, 5, 1165-1175, (2009) · Zbl 1162.93308 |

[20] | Vanek, B., Peni, T., Bokor, J., & Balas, G. (2005). Practical approach to real-time trajectory tracking of UAV formations. In Proc. of American control conference, Oregon (pp. 122-127). |

[21] | Wang, P.K.C., Navigation strategies for multiple autonomous mobile robots moving in formation, Journal of robotic systems, 8, 2, 177-195, (1991) · Zbl 0716.70035 |

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.