×

zbMATH — the first resource for mathematics

Sampled-data based average consensus of second-order integral multi-agent systems: switching topologies and communication noises. (English) Zbl 1319.93050
Summary: A distributed sampled-data based protocol is proposed for the average consensus of second-order integral multi-agent systems under switching topologies and communication noises. Under the proposed protocol, it is proved that sufficient conditions for ensuring mean square average consensus are: the consensus gain satisfies the stochastic approximation type condition and the communication topology graph at each sampling instant is a balanced graph with a spanning tree. Moreover, if the consensus gain takes some particular forms, the proposed protocol can solve the almost sure average consensus problem as well. Compared with the previous work, the distinguished features of this paper lie in that: (1) a sampled-data based stochastic approximation type protocol is proposed for the consensus of second-order integral multi-agent systems; (2) both communication noises and switching topologies are simultaneously considered; and (3) average consensus can be reached not only in the mean square sense but also in the almost sure sense.

MSC:
93C57 Sampled-data control/observation systems
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bullo, F.; Cortés, J.; Martínez, S., (Distributed control of robotic networks, Applied mathematics series, (2009), Princeton University Press)
[2] Cao, Y.; Ren, W., Sampled-data discrete-time coordination algorithms for double-integer dynamics directed interaction, International Journal of Control, 83, 3, 506-515, (2009) · Zbl 1222.93146
[3] Cheng, L.; Hou, Z.-G.; Lin, Y.; Tan, M.; Zhang, W., Solving a modified consensus problem of linear multi-agent systems, Automatica, 47, 10, 2218-2223, (2011) · Zbl 1228.93008
[4] Cheng, L.; Hou, Z.-G.; Tan, M.; Lin, Y.; Zhang, W., Neural-network-based adaptive leader-following control for multi-agent systems with uncertainties, IEEE Transactions on Neural Networks, 21, 8, 1351-1358, (2010)
[5] 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, 8, 1958-1963, (2011) · Zbl 1368.93659
[6] Chow, Y.; Teicher, H., Probability theory: independence, interchangeability, martingales, (1997), Springer New York · Zbl 0891.60002
[7] Hou, Z.-G.; Cheng, L.; Tan, M., Decentralized robust adaptive control for the multiagent system consensus problem using neural networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 39, 3, 636-647, (2009)
[8] Huang, M.; Dey, S.; Nair, G.; Manton, J., Stochastic consensus over noisy networks with Markovian and arbitrary switches, Automatica, 46, 10, 1571-1583, (2010) · Zbl 1204.93107
[9] 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, 1, 134-161, (2009) · Zbl 1182.93108
[10] Li, S.; Du, H.; Lin, X., Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics, Automatica, 47, 8, 1706-1712, (2011) · Zbl 1226.93014
[11] Li, T.; Zhang, J.-F., Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle, Science in China Series F: Information Sciences, 52, 11, 2089-2103, (2009) · Zbl 1182.93083
[12] 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
[13] 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
[14] Olfati-Saber, R.; Murray, R., Consensus problem in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[15] Qin, J.; Gao, H., A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays, IEEE Transactions on Automatic Control, 57, 9, 2417-2422, (2012) · Zbl 1369.93043
[16] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[17] Wang, X., & Hong, Y. (2008). Finite-time consensus for multi-agent networks with second-order agent dynamics. In Proceedings of IFAC world congress (pp. 15185-15190). Korea.
[18] Xiao, F.; Chen, T., Sampled-data consensus for multiple double integrators with arbitrary sampling, IEEE Transactions on Automatic Control, 57, 12, 3230-3235, (2012) · Zbl 1369.93057
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.