zbMATH — the first resource for mathematics

Consensus conditions of continuous-time multi-agent systems with additive and multiplicative measurement noises. (English) Zbl 1386.93281

93E03 Stochastic systems in control theory (general)
93E15 Stochastic stability in control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
94C15 Applications of graph theory to circuits and networks
Full Text: DOI
[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, A survey on sensor networks, IEEE Commun. Mag., 40 (2002), pp. 102–114.
[2] N. Amelina, A. Fradkov, Y. Jiang, and D. J. Vergados, Approximate consensus in stochastic networks with application to load balancing, IEEE Trans. Inform. Theory, 61 (2015), pp. 1739–1752. · Zbl 1359.90078
[3] J. A. Appleby, J. Cheng, and A. Rodkina, Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation, Discrete Contin. Dyn. Syst., Suppl. 1 (2011), pp. 79–90. · Zbl 1306.60066
[4] J. A. Appleby, J. P. Gleeson, and A. Rodkina, On asymptotic stability and instability with respect to a fading stochastic perturbation, Appl. Anal., 88 (2009), pp. 579–603. · Zbl 1168.60351
[5] T. C. Aysal and K. E. Barner, Convergence of consensus models with stochastic disturbances, IEEE Trans. Inform. Theory, 56 (2010), pp. 4101–4113. · Zbl 1366.93690
[6] Y. Cao, W. Yu, W. Ren, and G. Chen, An overview of recent progress in the study of distributed multi-agent coordination, IEEE Trans. Ind. Informat., 9 (2013), pp. 427–438.
[7] A. Carron, M. Todescato, R. Carli, and L. Schenato, An asynchronous consensus-based algorithm for estimation from noisy relative measurements, IEEE Trans. Control Netw. Syst., 1 (2014), pp. 283–295. · Zbl 1370.90064
[8] T. Chan and D. Williams, An “excursion” approach to an annealing problem, Math. Proc. Cambridge Philos. Soc., 105 (1989), pp. 169–176. · Zbl 0665.60058
[9] L. Cheng, Z.-G. Hou, and M. Tan, A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies, IEEE Trans. Automat. Control, 59 (2014), pp. 261–267. · Zbl 1360.93020
[10] H. Fang, H.-F. Chen, and L. Wen, On control of strong consensus for networked agents with noisy observations, J. Syst. Sci. Complex., 25 (2012), pp. 1–12. · Zbl 1251.93009
[11] H. Fourati, Multisensor Data Fusion: From Algorithms and Architectural Design to Applications, CRC Press, Boca Raton, FL, 2015.
[12] M. Huang, S. Dey, G. N. Nair, and J. H. Manton, Stochastic consensus over noisy networks with Markovian and arbitrary switches, Automatica J. IFAC, 46 (2010), pp. 1571–1583. · Zbl 1204.93107
[13] M. Huang and J. H. Manton, Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior, SIAM J. Control Optim., 48 (2009), pp. 134–161, . · Zbl 1182.93108
[14] M. Huang and J. H. Manton, Stochastic consensus seeking with noisy and directed inter-agent communication: Fixed and randomly varying topologies, IEEE Trans. Automat. Control, 55 (2010), pp. 235–241. · Zbl 1368.94002
[15] A. Jadbabaie, J. Lin, and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48 (2003), pp. 988–1001. · Zbl 1364.93514
[16] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer-Verlag, New York, 2002. · Zbl 0996.60001
[17] S. Kar and J. M. F. Moura, Distributed consensus algorithms in sensor networks with imperfect communication: Link failures and channel noise, IEEE Trans. Signal Process., 57 (2009), pp. 355–369. · Zbl 1391.94263
[18] N. E. Leonard and A. Olshevsky, Cooperative learning in multiagent systems from intermittent measurements, SIAM J. Control Optim., 53 (2015), pp. 1–29, . · Zbl 1336.93179
[19] T. Li, F. Wu, and J.-F. Zhang, Multi-agent consensus with relative-state-dependent measurement noises, IEEE Trans. Automat. Control, 59 (2014), pp. 2463–2468. · Zbl 1360.93033
[20] T. Li, F. Wu, and J.-F. Zhang, Continuous-time multi-agent averaging with relative-state-dependent measurement noises: Matrix intensity functions, IET Control Theory Appl., 9 (2015), pp. 374–380.
[21] T. Li and J.-F. Zhang, Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions, Automatica J. IFAC, 45 (2009), pp. 1929–1936. · Zbl 1185.93006
[22] T. Li and J.-F. Zhang, Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, IEEE Trans. Automat. Control, 55 (2010), pp. 2043–2057. · Zbl 1368.93548
[23] R. S. Lipster and A. N. Shiryayev, Theory of Martingales, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.
[24] J. Liu, X. Liu, W.-C. Xie, and H. Zhang, Stochastic consensus seeking with communication delays, Automatica J. IFAC, 47 (2011), pp. 2689–2696. · Zbl 1235.93013
[25] J. Liu, H. Zhang, X. Liu, and W.-C. Xie, Distributed stochastic consensus of multi-agent systems with noisy and delayed measurements, IET Control Theory Appl., 7 (2013), pp. 1359–1369.
[26] Y. Liu, K. M. Passino, and M. M. Polycarpou, Stability analysis of \(m\)-dimensional asynchronous swarms with a fixed communication topology, IEEE Trans. Automat. Control, 48 (2003), pp. 76–95. · Zbl 1364.93474
[27] Y. Long, S. Liu, and L. Xie, Distributed consensus of discrete-time multi-agent systems with multiplicative noises, Internat. J. Robust Nonlinear Control, 25 (2015), pp. 3113–3131. · Zbl 1327.93020
[28] X. Mao, Stochastic Differential Equations and Their Applications, Horwood Ser. Math. Appl., Horwood Publishing Ltd., Chichester, UK, 1997.
[29] S. Martin, A. Girard, A. Fazeli, and A. Jadbabaie, Multiagent flocking under general communication rule, IEEE Trans. Control Netw. Syst., 1 (2014), pp. 155–166. · Zbl 1370.93020
[30] L. Moreau, Stability of multi-agent systems with time-dependent communication links, IEEE Trans. Automat. Control, 50 (2005), pp. 169–182. · Zbl 1365.93268
[31] Y.-H. Ni and X. Li, Consensus seeking in multi-agent systems with multiplicative measurement noises, Systems Control Lett., 62 (2013), pp. 430–437. · Zbl 1276.93006
[32] M. Nourian, P. E. Caines, and R. P. Malhamé, A mean field game synthesis of initial mean consensus problems: A continuum approach for non-Gaussian behavior, IEEE Trans. Automat. Control, 59 (2014), pp. 449–455. · Zbl 1360.93049
[33] P. Ogren, E. Fiorelli, and N. E. Leonard, Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment, IEEE Trans. Automat. Control, 49 (2004), pp. 1292–1302. · Zbl 1365.93243
[34] R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95 (2007), pp. 215–233. · Zbl 1376.68138
[35] R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49 (2004), pp. 1520–1533. · Zbl 1365.93301
[36] Z. Qu, Cooperative Control of Dynamical systems: Applications to Autonomous Vehicles, Springer, London, 2009. · Zbl 1171.93005
[37] W. Ren and Y. Cao, Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues, Comm. Control Engrg., Springer-Verlag, London, 2011. · Zbl 1225.93003
[38] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd ed., Springer-Verlag, New York, 1999. · Zbl 0917.60006
[39] I. Saboori and K. Khorasani, \({H}_{∞ }\) consensus achievement of multi-agent systems with directed and switching topology networks, IEEE Trans. Automat. Control, 59 (2014), pp. 3104–3109. · Zbl 1360.93228
[40] J. S. Shamma, ed., Cooperative Control of Distributed Multi-Agent Systems, Wiley Online Library, John Wiley & Sons, Chichester, UK, 2007.
[41] H. Tang and T. Li, Continuous-time stochastic consensus: Stochastic approximation and Kalman-Bucy filtering based protocols, Automatica J. IFAC, 61 (2015), pp. 146–155. · Zbl 1327.93027
[42] B. Wang and J.-F. Zhang, Consensus conditions of multi-agent systems with unbalanced topology and stochastic disturbances, J. Systems Sci. Math. Sci., 29 (2009), pp. 1353–1365. · Zbl 1212.90072
[43] J. Wang and N. Elia, Distributed averaging under constraints on information exchange: Emergence of Lévy flights, IEEE Trans. Automat. Control, 57 (2012), pp. 2435–2449. · Zbl 1369.93704
[44] J. Wang and N. Elia, Mitigation of complex behavior over networked systems: Analysis of spatially invariant structures, Automatica J. IFAC, 49 (2013), pp. 1626–1638. · Zbl 1360.93059
[45] J. Xu, H. Zhang, and L. Xie, Stochastic approximation approach for consensus and convergence rate analysis of multiagent systems, IEEE Trans. Automat. Control, 57 (2012), pp. 3163–3168. · Zbl 1369.93058
[46] G. Yin, Y. Sun, and L. Y. Wang, Asymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies, Automatica J. IFAC, 47 (2011), pp. 1366–1378. · Zbl 1219.93117
[47] G. F. Young, L. Scardovi, and N. E. Leonard, Robustness of noisy consensus dynamics with directed communication, in American Control Conference (ACC), IEEE, 2010, pp. 6312–6317.
[48] X. Zong, F. Wu, G. Yin, and Z. Jin, Almost sure and \(p\)th-moment stability and stabilization of regime-switching jump diffusion systems, SIAM J. Control Optim., 52 (2014), pp. 2595–2622, . · Zbl 1390.34230
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.