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SCIENCE CHINA Information Sciences, Volume 61, Issue 7: 070216(2018) https://doi.org/10.1007/s11432-017-9407-6

Sliding mode control for consensus tracking of second-order nonlinear multi-agent systems driven by Brownian motion

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  • ReceivedAug 30, 2017
  • AcceptedMar 5, 2018
  • PublishedMay 31, 2018

Abstract

The consensus tracking problem of nonlinear stochastic multi-agent systems with directed topologies is investigated in this study. To solve the consensustracking problem, first, an innovative concept of sub-reachability is introduced, and then, the specified sliding hyperplane is designed. A novel consensus tracking protocol is then proposed by using sliding mode techniques. With the help of It$\hat{o}$ integral techniques and stochastic Lyapunov method, the sub-reachability of sliding motion and consensus tracking are proved; that is, the sliding mode variable structure control protocol steers the consensus errors to the given sliding surface in a finite time, and the sliding motion is exponentially stable in the sense of mean square.The efficacy of the proposed method is tested by a numerical case.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573154, 61573156), and partly supported by Science and Technology Project of Guangdong Province (Grant Nos. 2015A010106003, 2014A020217015).


References

[1] Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control, 2004, 49: 1520-1533 CrossRef Google Scholar

[2] Ren W, Beard R. Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Berlin: Springer, 2008. 125--136. Google Scholar

[3] Qin J, Gao H J, Zheng W X. Second-order consensus for multi-agent systems with switching topology and communication delay. Syst Control Lett, 2011, 60: 390-397 CrossRef Google Scholar

[4] Yu W W, Chen G R, Cao M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica, 2010, 46: 1089-1095 CrossRef Google Scholar

[5] Wen G, Duan Z S, Yu W W. Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications. Int J Control, 2013, 86: 322-331 CrossRef Google Scholar

[6] Su S Z, Lin Z L. Distributed consensus control of multi-agent systems with higher order agent dynamics and dynamically changing directed interaction topologies. IEEE Trans Autom Control, 2016, 61: 515-519 CrossRef Google Scholar

[7] Mu N K, Liao X F, Huang T. Consensus of second-order multi-agent systems with random sampling via event-triggered control. J Franklin Institute, 2016, 353: 1423-1435 CrossRef Google Scholar

[8] Yan H, Shen Y, Zhang H. Decentralized event-triggered consensus control for second-order multi-agent systems. Neurocomputing, 2014, 133: 18-24 CrossRef Google Scholar

[9] Zhu W, Pu H, Wang D H. Event-based consensus of second-order multi-agent systems with discrete time. Automatica, 2017, 79: 78-83 CrossRef Google Scholar

[10] Fan Y, Yang J. Average consensus of multi-agent systems with self-triggered controllers. Neurocomputing, 2016, 177: 33-39 CrossRef Google Scholar

[11] Yang D P, Ren W, Liu X. Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs. Automatica, 2016, 69: 242-249 CrossRef Google Scholar

[12] Huang M Y, Manton J H. Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. SIAM J Control Optim, 2009, 48: 134-161 CrossRef Google Scholar

[13] Huang M Y, Manton J H. Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies. IEEE Trans Autom Control, 2010, 55: 235-241 CrossRef Google Scholar

[14] Li T, Zhang J F. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Trans Autom Control, 2010, 55: 2043-2057 CrossRef Google Scholar

[15] Li T, Zhang J F. Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica, 2009, 45: 1929-1936 CrossRef Google Scholar

[16] Liu S J, Xie L H, Zhang H. Distributed consensus for multi-agent systems with delays and noises in transmission channels. Automatica, 2011, 47: 920-934 CrossRef Google Scholar

[17] Zhao B, Peng Y, Deng F. Consensus tracking for general linear stochastic multi-agent systems: a sliding mode variable structure approach. IET Control Theory Appl, 2017, 11: 2910-2915 CrossRef Google Scholar

[18] Utkin V I. Variable structure systems with sliding modes. IEEE Trans Autom Control, 1977, 22: 212-222 CrossRef Google Scholar

[19] Khoo S, Xie L H, Man Z H. Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Trans Mechatron, 2009, 14: 219-228 CrossRef Google Scholar

[20] Yin J L, Khoo S, Man Z. Finite-time stability and instability of stochastic nonlinear systems. Automatica, 2011, 47: 2671-2677 CrossRef Google Scholar

[21] Liu Y Q, Deng F Q. Variable Structure Control of Stochastic Systems. Guangzhou: South China University of Technology Press, 1998. Google Scholar

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