×

Stochastic averaging approach to leader-following consensus of linear multi-agent systems. (English) Zbl 1347.93024

Summary: Recently, consensus of high-order linear Multi-Agent Systems (MAS) has received much attention by many researchers, putting emphasis mainly on dealing with fixed network topology, with relatively few attention on the case of switching topology. The averaging method proposed in Ni et al. in 2012 and 2013 was shown to be a powerful tool to investigate consensus problem of deterministic switching high-order MAS. This paper aims at extending the deterministic averaging method to the stochastic case which includes communication white noises and Markovian switching network topology, where the commonly used assumptions in existing literature on the decreasing gain and the balance of the underlying graph were abandoned. The stochastic averaging based method can tackle the challenge problem of investigating the joint effect of the stochastic network topology, the high-order dynamics of the agents and the noisy communication among agents on the consensus. Extension to observer-based leader-following consensus is also explored and stochastic version of separation principle is obtained.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C05 Linear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aeyels, D.; Peuteman, J., On exponential stability of nonlinear time-varying differential equations, Automatica, 35, 63, 1091-1100, (1999) · Zbl 0931.93064
[2] Cheng, D.; Wang, J.; Hu, X., An extension of lasalle׳s invariance principle and its application to multi-agent consensus, IEEE Trans. Autom. Control, 53, 7, 1765-1770, (2008) · Zbl 1367.93427
[3] Cheng, L.; Hou, Z.; Tan, M.; Wang, X., Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises, IEEE Trans. Autom. Control, 56, 8, 1958-1963, (2011) · Zbl 1368.93659
[4] Z. Feng, G. Hu, G. Wen, Robust distributed consensus tracking for stochastic linear multi-agent systems under directed switching topologies, in: The 11-th IEEE International Conference on Control & Automation, Taichung, Taiwan, 2014, pp. 174-179.
[5] Freedman, D., Markov chains, (1983), Springer-Verlag New York · Zbl 0212.49801
[6] Fragoso, M. D.; Costa, O. L.V., A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Control Optim., 44, 4, 1165-1190, (2005) · Zbl 1139.93037
[7] Han, Y.; Lu, W.; Li, Z.; Chen, T., Pinning dynamic systems of networks with Markovian switching coupling and controller-node set, Syst. Control Lett., 65, 53-63, (2014) · Zbl 1285.93089
[8] Hong, Y.; Gao, L.; Cheng, D.; Hu, J., Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE Trans. Autom. Control, 52, 5, 943-948, (2007) · Zbl 1366.93437
[9] Hong, Y.; Hu, J.; Gao, L., Tracking control for multiagent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182, (2006) · Zbl 1117.93300
[10] Huang, M.; Manton, J. H., Coordination and consensus of networked agents with noisy measurementsstochastic algorithms and asymptotic behavior, SIAM J. Control Optim., 48, 1, 134-161, (2009) · Zbl 1182.93108
[11] Huang, M.; Dey, S.; Nair, G. N.; Manton, J. H., Stochastic consensus over noisy networks with Markovian and arbitrary switches, Automatica, 46, 10, 1571-1583, (2010) · Zbl 1204.93107
[12] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48, 6, 943-948, (2003) · Zbl 1364.93514
[13] Khasminskii, R. Z., Stability of regime-switching stochastic differential equations, Probl. Inf. Transm., 48, 3, 259-270, (2012) · Zbl 1259.60058
[14] Kirkilionis, M., An averaging principle for combined interaction graphsconnectivity and applications to genetic switches, Adv. Complex Syst., 13, 3, 293-326, (2013) · Zbl 1209.05255
[15] Kosut, R. L.; Anderson, B. D.O.; Mareels, I. M.Y., Stability theory for adaptive systems: method of averaging and persistency of excitation, IEEE Trans. Autom. Control, 32, 1, 26-34, (1987) · Zbl 0617.93047
[16] Li, W.; Xie, L.; Zhang, J., Containment control of leader-following multi-agent systems with Markovian switching network topologies and measurement noises, Automatica, 51, 263-267, (2015) · Zbl 1309.93012
[17] Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networksa unified viewpoint, IEEE Trans. Circuits Syst. - I: Regul. Pap., 57, 1, 213-224, (2010)
[18] Li, Z.; Duan, Z.; Chen, G., Dynamic consensus of linear multi-agent systems, IET Control Theory Appl., 5, 1, 19-28, (2011)
[19] Li, T.; Zhang, J.-F., Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises, IEEE Trans. Autom. Control, 55, 9, 2043-2057, (2010) · Zbl 1368.93548
[20] W. Liu, F. Deng, J. Liang, H. Ren, Mean square synchronization of nonlinear multi-agent systems under measurement noises, in: The 26-th Chinese Control and Decision Conference, Changsha, China, 2014, pp. 1153-1158.
[21] Ma, C.; Zhang, J., Necessary and sufficient conditions for consensusability of linear multi-agent systems, IEEE Trans. Autom. Control, 55, 5, 1263-1268, (2010) · Zbl 1368.93383
[22] Mariton, M., Jump linear systems in automatic control, (1990), Marcel Dekker New York
[23] Matei, I.; Baras, J. S., Convergence results for the linear consensus problem under Markovian random graphs, SIAM J. Control Appl., 51, 2, 1574-1591, (2013) · Zbl 1266.93137
[24] Ming, P.; Liu, J.; Tan, S.; Wang, G.; Shang, L.; Jia, C., Consensus stabilization of stochastic multi-agent system with Markovian switching topologies and stochastic communication noise, J. Frankl. Inst., 352, 9, 3684-3700, (2015) · Zbl 1395.93063
[25] Ni, W.; Cheng, D., Leader-following consensus of multi-agent systems under fixed and switching topologies, Syst. Control Lett., 59, 3-4, 209-217, (2010) · Zbl 1223.93006
[26] Ni, W.; Wang, Xiaoli; Xiong, Chun, Leader-following consensus of multiple linear systems under switching topologiesan averaging method, Kybernetika, 48, 6, 1194-1210, (2012) · Zbl 1255.93069
[27] Ni, W.; Wang, X.; Xiong, C., Consensus controllability, observability and robust design for leader-following linear multi-agent systems, Automatica, 49, 7, 2199-2205, (2013) · Zbl 1364.93072
[28] Ni, W.; Wang, X., Leader-following consensus of high-order multi-agent systems with bounded transmission channels, Int. J. Syst. Sci., 44, 9, 1711-1725, (2013) · Zbl 1278.93011
[29] Ni, Y.; Li, X., Consensus seeking in multi-agent systems with multiplicative measurement noises, Syst. Control Lett., 62, 5, 430-437, (2013) · Zbl 1276.93006
[30] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[31] Pavliotis, G. V.; Stuart, A. M., Multiscale methods: averaging and homogenization, (2008), Springer-Verlag New York · Zbl 1160.35006
[32] M. Porfiri, D.G. Roberson, D.J. Stilwell, Application of exponential splitting methods to fast switching theory, in: Proceedings of the 2006 America Control Conference, Minnesota, USA, 2006, pp. 5935-5940.
[33] Qu, Z., Cooperative control of dynamical systems: applications to autonomous vehicles, (2009), Springer-Verlag New York · Zbl 1171.93005
[34] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Autom. Control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[35] Shang, Y., Multi-agent coordination in directed moving neighborhood random networks, Chin. Phys. B, 19, 7, 070201, (2010)
[36] Shang, Y., Group pinning consensus under fixed and randomly switching topologies with acyclic partition, Netw. Heterog. Media, 9, 3, 553-573, (2014) · Zbl 1300.93017
[37] Shang, Y., Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies, J. Frankl. Inst., 352, 11, 4826-4844, (2015) · Zbl 1395.93068
[38] Shang, Y., Consensus of noisy multiagent systems with Markovian switching topologies and time-varying delays, Math. Probl. Eng., 2015, (2015), article id: 453072 · Zbl 1394.93116
[39] Shang, Y., Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies, Appl. Math. Comput., 273, 1234-1245, (2016) · Zbl 1410.93113
[40] Wang, X.; Hong, Y.; Huang, J.; Jiang, Z., A distributed control approach to a robust output regulation problem for multi-agent linear systems, IEEE Trans. Autom. Control, 55, 12, 2891-2895, (2010) · Zbl 1368.93577
[41] Wang, Y.; Cheng, L.; Ren, W.; Hou, Z.-G.; Tan, M., Seeking consensus in networks of linear agentscommunication noises and Markovian switching topologies, IEEE Trans. Autom. Control, 60, 5, 1374-1379, (2015) · Zbl 1360.93753
[42] You, K.; Li, Z.; Xie, L., Consensus condition for linear multi-agent systems over randomly switching topologies, Automatica, 49, 10, 3125-3132, (2013) · Zbl 1358.93025
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.