Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays.

*(English)*Zbl 1393.93014Summary: We study the consensus control of discrete-time second-order multi-agents systems with time delays and multiplicative noises, where the consensus protocol is designed by both the local relative position measurements and each agent’s absolute velocity. Due to the existence of time delays and multiplicative noises, the classical methods for deterministic models with time delays cannot work. In this paper, we apply stochastic stability theorem of discrete-time stochastic delay equations to find some explicit sufficient conditions for both mean square and almost sure consensus. It is proven that for any given noise intensities and time delays, the second-order multi-agent consensus can be achieved by choosing appropriate control gains in the relative position measurement and absolute velocity, respectively. Numerical simulation is given to demonstrate the effectiveness of the proposed protocols as well as the theoretical results.

##### MSC:

93A14 | Decentralized systems |

93C55 | Discrete-time control/observation systems |

68T42 | Agent technology and artificial intelligence |

93E15 | Stochastic stability in control theory |

##### Keywords:

consensus control; discrete-time second-order multi-agents systems; time delays; multiplicative noises
PDF
BibTeX
XML
Cite

\textit{Y. Zhang} et al., J. Franklin Inst. 355, No. 5, 2791--2807 (2018; Zbl 1393.93014)

Full Text:
DOI

##### References:

[1] | Qu, Z., Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, (2009), Springer London · Zbl 1171.93005 |

[2] | Attoui, A., Real-time and Multi-agent Systems, (2012), Springer Science & Business Media London |

[3] | Uhrmacher, A. M.; Weyns, D., Multi-agent systems: simulation and applications, (2009), CRC press London |

[4] | Ogren, P.; Fiorelli, E.; Leonard, N. E., Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment, IEEE Trans. Autom. Control, 49, 8, 1292-1302, (2004) · Zbl 1365.93243 |

[5] | Cao, Y.; Yu, W.; Ren, W.; Chen, G., An overview of recent progress in the study of distributed multi-agent coordination, IEEE Trans. Ind. Inf., 9, 1, 427-438, (2013) |

[6] | Schenato, L.; Fiorentin, F., Average timesynch: a consensus-based protocol for clock synchronization in wireless sensor networks, Automatica, 47, 9, 1878-1886, (2011) · Zbl 1223.68022 |

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

[8] | Shamma, J. S., Cooperative Control of Distributed Multi-Agent Systems, (2007), Wiley Online Library Hoboken |

[9] | Li, T.; Fu, M.; Xie, L.; Zhang, J.-F., Distributed consensus with limited communication data rate, IEEE Trans. Autom. Control, 56, 2, 279-292, (2011) · Zbl 1368.93346 |

[10] | Leonard, N. E.; Olshevsky, A., Cooperative learning in multiagent systems from intermittent measurements, SIAM J. Control Optim., 53, 1, 1-29, (2015) · Zbl 1336.93179 |

[11] | Munz, U.; Papachristodoulou, A.; Allgower, F., Consensus in multi-agent systems with coupling delays and switching topology, IEEE Trans. Autom. Control, 56, 12, 2976-2982, (2011) · Zbl 1368.93010 |

[12] | Sakurama, K.; Nakano, K., Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays, Int. J. Syst. Sci., 46, 5, 818-830, (2015) · Zbl 1312.93012 |

[13] | Cepeda-Gomez, R.; Olgac, N., A consensus protocol under directed communications with two time delays and delay scheduling, Int. J. Control, 87, 2, 291-300, (2014) · Zbl 1317.93009 |

[14] | Hadjicostis, C.; Charalambous, T., Average consensus in the presence of delays in directed graph topologies, IEEE Trans. Autom. Control, 59, 3, 763-768, (2014) · Zbl 1360.93027 |

[15] | Cheng, L.; Hou, Z.-G.; Tan, M., A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies, IEEE Trans. Autom. Control, 59, 1, 261-267, (2014) · Zbl 1360.93020 |

[16] | Li, T.; Wu, F.; Zhang, J.-F., Multi-agent consensus with relative-state-dependent measurement noises, IEEE Trans. Autom. Control, 59, 9, 2463-2468, (2014) · Zbl 1360.93033 |

[17] | Zong, X.; Li, T.; Zhang, J.-F., Stochastic consensus of linear multi-agent systems with multiplicative measurement noises, Proceedings of the Twelfth IEEE International Conference on Control & Automation (ICCA), 7-12, (2016), Kathmandu, Nepal |

[18] | X. Zong, T. Li, J.-F. Zhang, Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises, arXiv:1602.00069. · Zbl 1386.93281 |

[19] | Li, T.; Zhang, J.-F., Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, IEEE Trans. Autom. Control, 55, 9, 2043-2057, (2010) · Zbl 1368.93548 |

[20] | Zong, X.; Li, T.; Zhang, J.-F., Stochastic consensus of continuous-time multi-agent systems with additive measurement noises, Proceedings of the IEEE Fifty-Fourth Annual Conference on Decision and Control, 543-548, (2015), Osaka, Japan |

[21] | Liu, J.; Zhang, H.; Liu, X.; Xie, W.-C., Distributed stochastic consensus of multi-agent systems with noisy and delayed measurements, IET Control Theory Appl., 7, 10, 1359-1369, (2013) |

[22] | Lin, P.; Ren, W., Constrained consensus in unbalanced networks with communication delays, IEEE Trans. Autom. Control, 59, 3, 775-781, (2014) · Zbl 1360.93037 |

[23] | Huang, M.; Manton, J., Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior, SIAM J. Control Optim., 48, 1, 134-161, (2009) · Zbl 1182.93108 |

[24] | Ni, Y.-H.; Li, X., Consensus seeking in multi-agent systems with multiplicative measurement noises, Syst. Control Lett., 62, 5, 430-437, (2013) · Zbl 1276.93006 |

[25] | Long, Y.; Liu, S.; Xie, L., Distributed consensus of discrete-time multi-agent systems with multiplicative noises, Int. J. Robust Nonlinear Control, 25, 5, 3113-3131, (2015) · Zbl 1327.93020 |

[26] | Long, Y.; Liu, S.; Xie, L., Consensus of discrete multi-agent systems with multiplicative noises, Proceedings of the Eleventh IEEE International Conference on Control & Automation (ICCA), 255-260, (2014), IEEE |

[27] | Liu, J.; Liu, X.; Xie, W.-C.; Zhang, H., Stochastic consensus seeking with communication delays, Automatica, 47, 12, 2689-2696, (2011) · Zbl 1235.93013 |

[28] | Liu, S.; Xie, L.; Zhang, H., Distributed consensus for multi-agent systems with delays and noises in transmission channels, Automatica, 47, 5, 920-934, (2011) · Zbl 1233.93007 |

[29] | Zong, X.; Wu, F.; Yin, G.; Jin, Z., Almost sure and pth-moment stability and stabilization of regime-switching jump diffusion systems, SIAM J. Control Optim., 52, 4, 2595-2622, (2014) · Zbl 1390.34230 |

[30] | Park, M. J.; Kwon, O. M.; Park, J. H.; Lee, S. M.; Son, J. W.; Cha, E., \(\mathcal{H}_\infty\) consensus performance for discrete-time multi-agent systems with communication delay and multiple disturbances, Neurocomputing, 138, 199-208, (2014) |

[31] | Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, Int. J. Robust Nonlinear Control, 17, 1002-1033, (2007) · Zbl 1266.93010 |

[32] | Qin, J.; Gao, H.; Zheng, W. X., Second-order consensus for multi-agent systems with switching topology and communication delay, Syst. Control Lett., 60, 390-397, (2011) · Zbl 1225.93020 |

[33] | Dong, X.; Li, Q.; Wang, R.; Ren, Z., Time-varying formation control for second-order swarm systems with switching directed topologies, Inf. Sci., 369, 1-13, (2016) |

[34] | Li, H.; Chen, G.; Dong, Z.; Xia, D., Consensus analysis of multiagent systems with second-order nonlinear dynamics and general directed topology: an event-triggered scheme, Inf. Sci., 370-371, 598-622, (2016) |

[35] | Liu, C.-L.; Liu, F., Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation, Syst. Control Lett., 61, 1235-1241, (2012) · Zbl 1255.93010 |

[36] | Xie, D.; Liang, T., Second-order group consensus for multi-agent systems with time delays, Neurocomputing, 153, 133-139, (2015) |

[37] | Liu, B.; Wang, X.; Su, H.; Gao, Y.; Wang, L., Adaptive second-order consensus of multi-agent systems with heterogeneous nonlinear dynamics and time-varying delays, Neurocomputing, 118, 289-300, (2013) |

[38] | Sun, Y.; Wang, L., H_{∞} consensus of second-order multi-agent systems with asymmetric delays, Syst. Control Lett., 61, 857-862, (2012) · Zbl 1252.93049 |

[39] | Li, W.; Li, T.; Xie, L.; Zhang, J.-F., Distributed tracking of second-order multi-agent systems with measurement noise, Proceedings of the Ninth IEEE International Conference on Control and Automation (ICCA), 12-14, (2013), Hangzhou, China |

[40] | Cheng, L.; Hou, Z.-G.; Tan, M.; Wang, X., Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises, IEEE Trans. Autom. Control, 56, 8, 1958-1963, (2011) · Zbl 1368.93659 |

[41] | Djaidja, S.; Wu, Q.; Fang, H., Consensus of double-integrator multi-agent systems without relative state derivatives under communication noises and directed topologies, J. Frankl. Inst., 325, 897-912, (2015) · Zbl 1307.93373 |

[42] | Lin, P.; Jia, Y., Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 2154-2158, (2009) · Zbl 1175.93078 |

[43] | Gao, Y.; Ma, J.; Zuo, M.; Jiang, T.; Du, J., Consensus of discrete-time second-order agents with time-varying topology and time-varying delays, J. Frankl. Inst., 349, 2598-2608, (2012) · Zbl 1300.93013 |

[44] | Zong, X.; Li, T.; Zhang, J.-F., Consensus control of discrete-time multi-agent systems with time-delays and multiplicative measurement noises (in Chinese), SCIENTIA SINICA Math., 46, 10, 1617-1636, (2016) |

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.