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Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises. (English) Zbl 1406.93046
Summary: This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations. By the martingale convergence theorem, we obtain necessary conditions and sufficient conditions for stochastic strong consensus. For the case of multiplicative noises, we consider two kinds of time-delays, appeared in the measurement term and the noise term, respectively. We first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus. Then by constructing degenerate Lyapunov functional, we find sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time-delay in the measurement term.

MSC:
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93E03 Stochastic systems in control theory (general)
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[1] Akyildiz, I. F.; Su, W.; Sankarasubramaniam, Y.; Cayirci, E., A survey on sensor networks, IEEE Communications Magazine, 40, 102-114, (2002)
[2] Amelina, N.; Fradkov, A.; Jiang, Y.; Vergados, D. J., Approximate consensus in stochastic networks with application to load balancing, IEEE Transactions on Information Theory, 61, 1739-1752, (2015) · Zbl 1359.90078
[3] Aysal, T. C.; Barner, K. E., Convergence of consensus models with stochastic disturbances, IEEE Transactions on Information Theory, 56, 4101-4113, (2010) · Zbl 1366.93690
[4] Carlia, R.; Fagnanib, F., Communication constraints in the average consensus problem, Automatica, 44, 671-684, (2008)
[5] Cepeda-Gomez, R.; Olgac, N., An exact method for the stability analysis of linear consensus protocols with time delay, IEEE Transactions on Automatic Control, 56, 1734-1740, (2011) · Zbl 1368.93591
[6] 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 Transactions on Automatic Control, 56, 1958-1963, (2011) · Zbl 1368.93659
[7] Dimarogonas, D. V.; Johansson, K. H., Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control, Automatica, 46, 695-700, (2010) · Zbl 1193.93059
[8] Gripenberg, G.; Londen, S.-O.; Staffans, O., Volterra integral and functional equations, (1990), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0695.45002
[9] Grossman, S. E.; Yorke, J. A., Asymptotic behavior and exponential stability criteria for differential delay equations, Journal of Differential Equations, 12, 236-255, (1972) · Zbl 0268.34079
[10] Hadjicostis, C. N.; Charalambous, T., Average consensus in the presence of delays in directed graph topologies, IEEE Transactions on Automatic Control, 59, 763-768, (2014) · Zbl 1360.93027
[11] Hale, J. K.; Lunel, J. M.V., Introduction to functional differential equations, (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002
[12] Huang, M.; Dey, S.; Nair, G. N.; Manton, J. H., Stochastic consensus over noisy networks with markovian and arbitrary switches, Automatica, 46, 1571-1583, (2010) · Zbl 1204.93107
[13] Huang, M.; Manton, J., Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior, SIAM Journal on Control and Optimization, 48, 134-161, (2009) · Zbl 1182.93108
[14] Kar, S.; Moura, J. M., Distributed consensus algorithms in sensor networks with imperfect communication: Link failures and channel noise, IEEE Transactions on Signal Processing, 57, 355-369, (2009) · Zbl 1391.94263
[15] Kolmanovskii, V.; Myshkis, A., Applied theory of functional differential equations, (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0917.34001
[16] Li, T.; Wu, F.; Zhang, J.-F., Multi-agent consensus with relative-state-dependent measurement noises, IEEE Transactions on Automatic Control, 59, 2463-2468, (2014) · Zbl 1360.93033
[17] Li, T.; Zhang, J.-F., Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions, Automatica, 45, 1929-1936, (2009) · Zbl 1185.93006
[18] 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, 2043-2057, (2010) · Zbl 1368.93548
[19] Lin, P.; Ren, W., Constrained consensus in unbalanced networks with communication delays, IEEE Transactions on Automatic Control, 59, 775-781, (2014) · Zbl 1360.93037
[20] Liu, S.; Li, T.; Xie, L., Distributed consensus for multiagent systems with communication delays and limited data rate, SIAM Journal on Control and Optimization, 49, 2239-2262, (2011) · Zbl 1234.68034
[21] Liu, J.; Liu, X.; Xie, W.-C.; Zhang, H., Stochastic consensus seeking with communication delays, Automatica, 47, 2689-2696, (2011) · Zbl 1235.93013
[22] Liu, Y.; Passino, K. M.; Polycarpou, M. M., Stability analysis of \(m\)-dimensional asynchronous swarms with a fixed communication topology, IEEE Transactions on Automatic Control, 48, 76-95, (2003) · Zbl 1364.93474
[23] Liu, S.; Xie, L.; Zhang, H., Distributed consensus for multi-agent systems with delays and noises in transmission channels, Automatica, 47, 920-934, (2011) · Zbl 1233.93007
[24] Long, Y.; Liu, S.; Xie, L., Distributed consensus of discrete-time multi-agent systems with multiplicative noises, International Journal of Robust & Nonlinear Control, 25, 3113-3131, (2015) · Zbl 1327.93020
[25] Mao, X., Stochastic differential equations and their applications, (1997), Horwood Publishing Limited: Horwood Publishing Limited Chichester
[26] Martin, S.; Girard, A.; Fazeli, A.; Jadbabaie, A., Multiagent flocking under general communication rule, IEEE Transactions on Control of Network Systems, 1, 155-166, (2014) · Zbl 1370.93020
[27] Munz, U.; Papachristodoulou, A.; Allgower, F., Consensus in multi-agent systems with coupling delays and switching topology, IEEE Transactions on Automatic Control, 56, 2976-2982, (2011) · Zbl 1368.93010
[28] Ni, Y.-H.; Li, X., Consensus seeking in multi-agent systems with multiplicative measurement noises, Systems & Control Letters, 62, 430-437, (2013) · Zbl 1276.93006
[29] Ogren, P.; Fiorelli, E.; Leonard, N. E., Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment, IEEE Transactions on Automatic Control, 49, 1292-1302, (2004) · Zbl 1365.93243
[30] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 1520-1533, (2004) · Zbl 1365.93301
[31] Sakurama, K.; Nakano, K., Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays, International Journal of Systems Science, 46, 818-830, (2015) · Zbl 1312.93012
[32] Tahbaz-Salehi, A.; Jadbabaie, A., A necessary and sufficient condition for consensus over random networks, IEEE Transactions on Automatic Control, 53, 791-795, (2008) · Zbl 1367.90015
[33] Tang, H.; Li, T., Continuous-time stochastic consensus: Stochastic approximation and kalmancbucy filtering based protocols, Automatica, 61, 146-155, (2015) · Zbl 1327.93027
[34] Tuzlukov, V. P., Signal processing noise, (2002), CRC Press: CRC Press Boca Raton
[35] Wang, J.; Elia, N., Mitigation of complex behavior over networked systems: Analysis of spatially invariant structures, Automatica, 49, 1626-1638, (2013) · Zbl 1360.93059
[36] Wang, B.; Zhang, J.-F., Consensus conditions of multi-agent systems with unbalanced topology and stochastic disturbances, Journal of Systems Science and Mathematical Sciences, 29, 1353-1365, (2009) · Zbl 1212.90072
[37] Wang, Z.; Zhang, H.; Fu, M.; Zhang, H., Consensus for high-order multi-agent systems with communication delay, Science China: Information Sciences, 60, 092204, (2017)
[38] Xu, J.; Zhang, H.; Xie, L., Stochastic approximation approach for consensus and convergence rate analysis of multiagent systems, IEEE Transactions on Automatic Control, 57, 3163-3168, (2012) · Zbl 1369.93058
[39] Xu, J.; Zhang, H.; Xie, L., Input delay margin for consensusability of multi-agent systems, Automatica, 49, 1816-1820, (2013) · Zbl 1360.93065
[40] Zhu, B.; Xie, L.; Han, D.; Meng, X.; Teo, R., A survey on recent progress in control of swarm systems, Science China: Information Sciences, 60, 070201, (2017)
[41] Zong, X., Li, T., & Zhang, J.-F. (2017). Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises, arXiv:1602.00069.
[42] Zong, X.; Li, T.; Zhang, J.-F., Consensus conditions for continuous-time multi-agent systems with additive and multiplicative measurement noises, SIAM Journal on Control and Optimization, 56, 19-52, (2018) · Zbl 1386.93281
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