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Consensus of discrete-time multi-agent systems with multiplicative uncertainties and delays. (English) Zbl 1483.93594

Summary: This paper studies the consensus problem of discrete-time single-integrator multi-agent systems with multiplicative uncertainties and bounded communication delays in switching networks. Some sufficient conditions for non-stochastic consensus are obtained by adopting the constant-gain protocol. For the case that the uncertainty is exponentially decaying (i.e. is \(O(\gamma^k)\) with \(\gamma \in (0,1))\), it is proved for any bounded delays, the consensus can be achieved if the switching topology is uniformly rooted. For the case that the uncertainty is polynomially decaying (i.e. is \(O(\frac{1}{(1+k)^\mu})\) with \(\mu > 0)\), under a precondition that the system state is bounded, a similar conclusion is also obtained. The convergence rate of the consensus protocol is quantified in terms of the decay rate of uncertainties. Simulation results are given to verify the correctness of the conclusion.

MSC:

93D50 Consensus
93C55 Discrete-time control/observation systems
93A16 Multi-agent systems
93C43 Delay control/observation systems
93C41 Control/observation systems with incomplete information

Software:

DILAND
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abbott, S., Understanding analysis, Vol. 2 (2001), Springer New York · Zbl 0966.26001
[2] Cao, M.; Morse, A. S.; Anderson, B. D. O., Reaching a consensus in a dynamically changing environment: Convergence rates, measurement delays, and asynchronous events, SIAM Journal on Control and Optimization, 47, 2, 601-623 (2008) · Zbl 1157.93434
[3] Carli, R., D’Elia, E., & Zampieri, S (2011). A PI controller based on asymmetric gossip communications for clocks synchronization in wireless sensors networks. Proceedings of 50st IEEE Conference on Decision and Control and European Control Conference (pp. 7512-7517). IEEE. doi:10.1109/CDC.2011.6161101
[4] Huang, M.; Manton, J. H., Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior, SIAM Journal on Control and Optimization, 48, 1, 134-161 (2009) · Zbl 1182.93108
[5] 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
[6] Khan, U. A.; Kar, S.; Moura, J. F., DILAND: An algorithm for distributed sensor localization with noisy distance measurements, IEEE Transactions on Signal Processing, 58, 3, 1940-1947 (2010) · Zbl 1392.94628
[7] Li, T.; Wu, F.; Zhang, J. F., Multi-agent consensus with relative-state-dependent measurement noises, IEEE Transactions on Automatic Control, 59, 9, 2463-2468 (2014) · Zbl 1360.93033
[8] Li, T.; Zhang, J. F., Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, IEEE Transactions on Automatic Control, 55, 9, 2043-2057 (2010) · Zbl 1368.93548
[9] Lin, Z.; Han, T.; Zheng, R.; Fu, M., Distributed localization for 2-D sensor networks with bearing-only measurements under switching topologies, IEEE Transactions on Signal Processing, 64, 23, 6345-6359 (2016) · Zbl 1414.94349
[10] Lin, P.; Jia, Y., Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 9, 2154-2158 (2009) · Zbl 1175.93078
[11] 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
[12] Ma, L.; Wang, Z.; Han, Q. L.; Liu, Y., Consensus control of stochastic multi-agent systems: A survey, Science China Information Sciences, 60, 12, 120201:1-120201:15 (2017)
[13] Oh, K. K.; Ahn, H. S., Formation control and network localization via orientation alignment, IEEE Transactions on Automatic Control, 59, 2, 540-545 (2014) · Zbl 1360.93052
[14] 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
[15] Qi, T.; Qiu, L.; Chen, J., MAS consensus and delay limits under delayed output feedback, IEEE Transactions on Automatic Control, 62, 9, 4660-4666 (2016) · Zbl 1390.93072
[16] Qin, J.; Ma, Q.; Shi, Y.; Wang, L., Recent advances in consensus of multi-agent systems: A brief survey, IEEE Transactions on Industrial Electronics, 64, 6, 4972-4983 (2017)
[17] 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
[18] Savino, H. J.; Souza, F.; Pimenta, L. C., Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays, International Journal of Systems Science, 47, 10, 2475-2486 (2016) · Zbl 1345.93014
[19] 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
[20] Song, L.; Huang, D.; Nguang, S. K.; Fu, S., Mean square consensus of multi-agent systems with multiplicative noises and time delays under directed fixed topologies, International Journal of Control and Automation, 14, 1, 69-77 (2016)
[21] Sun, F.; Guan, Z. H.; Ding, L.; Wang, Y. W., Mean square average-consensus for multi-agent systems with measurement noise and time delay, International Journal of Systems Science, 44, 6, 995-1005 (2013) · Zbl 1278.93015
[22] Tian, Y. P. (2015). LSTS: A new time synchronization protocol for networks with random communication delays. Proceedings of 54st IEEE Conference on Decision and Control (pp. 7404-7409). IEEE. doi:10.1109/CDC.2015.7403389
[23] Tian, Y. P. (2016). Consensus with noisy information. Proceedings of 35th Chinese Control Conference (pp. 7769-7774). IEEE. doi:10.1109/ChiCC.2016.7554589
[24] Tian, Y. P., Time synchronization in WSNs with random bounded communication delays, IEEE Transactions on Automatic Control, 62, 10, 5445-5450 (2017) · Zbl 1390.68080
[25] Tian, Y. P.; Zong, S.; Cao, Q., Structural modeling and convergence analysis of consensus-based time synchronization algorithms over networks: Non-topological conditions, Automatica, 65, 64-75 (2016) · Zbl 1328.93034
[26] Wang, B.; Tian, Y. P., Time synchronization in WSNs with random communication delays: A constant gain design, IFAC-PapersOnLine, 50, 1, 657-662 (2017)
[27] Wang, B.; Tian, Y. P., Distributed network localization: Accurate estimation with noisy measurement and communication information, IEEE Transactions on Signal Processing, 66, 22, 5927-5940 (2018) · Zbl 1415.94268
[28] Wu, F., Tian, Y. P., & Wang, B (2017). Distributed localization in sensor networks with communication and measurement noises. Proceedings of 11th Asian Control Conference (pp. 1962-1967). IEEE. doi:10.1109/ASCC.2017.8287475
[29] Xiao, F.; Wang, L., State consensus for multi-agent systems with switching topologies and time-varying delays, International Journal of Control, 79, 10, 1277-1284 (2006) · Zbl 1330.94022
[30] Yıldırım, K. S.; Carli, R.; Schenato, L., Adaptive proportional-integral clock synchronization in wireless sensor networks, IEEE Transactions on Control Systems Technology, 26, 2, 610-623 (2018)
[31] Zong, X.; Li, T.; Zhang, J., Consensus control of discrete-time multi-agent systems with time delays and multiplicative measurement noises, Science in China Series A - Mathematics, 46, 10, 1617-1636 (2016) · Zbl 1499.93072
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