zbMATH — the first resource for mathematics

Distributed consensus of discrete-time multi-agent systems with multiplicative noises. (English) Zbl 1327.93020
Summary: In this paper, we consider the consensus problem of discrete-time multi-agent systems with multiplicative communication noises. Each agent can only receive information corrupted by noises from its neighbors and/or a reference node. The intensities of these noises are dependent on the relative states of agents. Under some mild assumptions of the noises and the structure of network, consensus is analyzed under a fixed topology, dynamically switching topologies and randomly switching topologies, respectively. By combining algebraic graph theory and martingale convergence theorem, sufficient conditions for mean square and almost sure consensus are given. Further, when the consensus is achieved without a reference, it is shown that the consensus point is a random variable with its expectation being the average of the initial states of the agents and its variance being bounded. If the multi-agent system has access to the state of the reference, the state of each agent can asymptotically converge to the reference. Numerical examples are given to illustrate the effectiveness of our results.

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93E03 Stochastic systems in control theory (general)
Full Text: DOI
[1] Attiya, Distributed Computing: Fundamentals, Simulations, and Advanced Topics (2004)
[2] Xiao, Finite-time formation control for multi-agent systems, Automatica 45 (11) pp 2605– (2009) · Zbl 1180.93006
[3] Xiao L Boyd S Lall S A scheme for robust distributed sensor fusion based on average consensus International Symposium on Information Processing in Sensor Networks, Los Angles, CA 2005 63 70
[4] Hu, Cooperative search and exploration in robotic networks, Unmanned Systems 01 (01) pp 121– (2013)
[5] Kopeikin, Dynamic mission planning for communication control in multiple unmanned aircraft teams, Unmanned Systems 01 (01) pp 41– (2013)
[6] Olfati-Saber R Shamma JS Consensus filters for sensor networks and distributed sensor fusion 44th IEEE Conference on Decision and Control and European Control Conference, Seville 2005 6698 6703
[7] Olfati-Saber, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control 49 (9) pp 1520– (2004) · Zbl 1365.93301
[8] Kingston DB Beard RW Discrete-time average-consensus under switching network topologies Minneapolis, MN 2006 3551 3556
[9] Hong, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42 (7) pp 1177– (2006) · Zbl 1117.93300
[10] Lin, Average consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A: Statistical Mechanics and its Applications 387 (1) pp 303– (2008)
[11] Lin, Distributed robust h consensus control in directed networks of agents with time-delay, Systems & Control Letters 57 (8) pp 643– (2008) · Zbl 1140.93355
[12] Liu, Distributed consensus for multi-agent systems with delays and noises in transmission channels, Automatica 47 (5) pp 920– (2011) · Zbl 1233.93007
[13] Huang, Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior, SIAM Journal on Control and Optimization 48 (1) pp 134– (2009) · Zbl 1182.93108
[14] Li, Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, IEEE Transactions on Automatic Control 55 (9) pp 2043– (2010) · Zbl 1368.93548
[15] Ransom, A discrete receiver structure for bit detection without synchronization for signals corrupted by additive and multiplicative noise, IEEE Transactions on Communications 22 (10) pp 1702– (1974)
[16] Dogandzic, Space-time fading channel estimation and symbol detection in unknown spatially correlated noise, IEEE Transactions on Signal Processing 50 (3) pp 457– (2002)
[17] Elia, Remote stabilization over fading channels, Systems & Control Letters 54 (3) pp 237– (2005) · Zbl 1129.93498
[18] Nabar, Fading relay channels: Performance limits and space-time signal design, IEEE Journal on Selected Areas in Communications 22 (6) pp 1099– (2004)
[19] Xiao, Feedback stabilization of discrete-time networked systems over fading channels, IEEE Transactions on Automatic Control 57 (9) pp 2176– (2012) · Zbl 1369.93708
[20] Patterson, Convergence rates of distributed average consensus with stochastic link failures, IEEE Transactions on Automatic Control 55 (4) pp 880– (2010) · Zbl 1368.94198
[21] Li, Multi-agent consensus with relative-state-dependent measurement noises, IEEE Transactions on Automatic Control PP (99) pp 1– (2014)
[22] Ni, Consensus seeking in multi-agent systems with multiplicative measurement noises, Systems & Control Letters 62 (5) pp 430– (2013) · Zbl 1276.93006
[23] Ren, Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications (2008) · Zbl 1144.93002
[24] Williams, Probability with Martingales (1991) · Zbl 0722.60001
[25] Liu, Continuous-time and sampled-data based average consensus with logarithmic quantizers, Automatica 49 (11) pp 3329– (2013) · Zbl 1315.93005
[26] Bhatia, Matrix Analysis (1997)
[27] Olfati-Saber R Distributed tracking for mobile sensor networks with information-driven mobility American Control Conference, New York, NY 2007 4606 4612
[28] Huang B Xie L Yang Z Analysis of TOA localization with heteroscedastic noises. Chinese Control Conference, 2014
[29] Lanzisera, Radio frequency time-of-flight distance measurement for low-cost wireless sensor localization, IEEE Sensors Journal 11 (3) pp 837– (2011)
[30] Chow, Probability theory: independence, interchangeability, martingales (2003) · Zbl 1049.60001
[31] Li T Asymptotically unbiased average consensus under measurement noises and fixed topologies Proceedings of the 17th IFAC World Congress, COEX, South Korea 2008 2867 2873
[32] Di Cairano S Pasini A Bemporad A Murray RM Convergence properties of dynamic agents consensus networks with broken links American Control Conference, Seattle, WA 2008 1362 1367
[33] Fagnani, Average consensus with packet drop communication, SIAM Journal on Control and Optimization 48 (1) pp 102– (2009) · Zbl 1216.05143
[34] Vaidya NH Hadjicostis CN Dominguez-Garcia AD Robust average consensus over packet dropping links: Analysis via coefficients of ergodicity 2012 IEEE 51st Annual Conference on Decision and Control, Maui, HI 2012 2761 2766
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.