带随机扰动的耦合谐振子网络系统的同步
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摘要
研究了一种带随机扰动输入项的耦合谐振子网络系统的同步动力学。针对实际工程应用中数据难免带有各种随机扰动等现象,基于相对位移信息耦合优点,设计了一个在一般条件下适用的分布式控制输入协议。利用随机微分方程的稳定性理论以及伊藤(It?)公式等工具,分析了耦合谐振子网络系统在这个协议下的同步动力学,得到了系统达到几乎处处同步的一个充分条件。数值模拟进一步验证了该理论结果的正确性和协议的有效性。
In this paper,the synchronization dynamics of a networked harmonic oscillators system with stochastic input terms was studied. Aiming at the stochastic perturbation of data in practical engineering application,a distributed control input protocol was designed based on the advantage of relative displacement information coupling. By using the stability theory of stochastic differential equation and It? formula,the synchronization dynamics of networked harmonic oscillators system under this protocol is analyzed,and a sufficient condition for the system to achieve almost surely synchronization is obtained. The numerical simulations further verify the correctness of the theoretical results and the effectiveness of the protocol.
In this paper,the synchronization dynamics of a networked harmonic oscillators system with stochastic input terms was studied. Aiming at the stochastic perturbation of data in practical engineering application,a distributed control input protocol was designed based on the advantage of relative displacement information coupling. By using the stability theory of stochastic differential equation and It? formula,the synchronization dynamics of networked harmonic oscillators system under this protocol is analyzed,and a sufficient condition for the system to achieve almost surely synchronization is obtained. The numerical simulations further verify the correctness of the theoretical results and the effectiveness of the protocol.
引文
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[3]JAIN A,GHOSE D.Synchronization of multi-agent systems with heterogeneous controllers[J].Nonlinear Dynamics,2017,89(2):1-19.
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[6]DONG H,YE D,FENG J,and et al.Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control[J].Nonlinear Dynamics,2017,87(2):727-739.
[7]WANG J,FENG J,XU C,et al.Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix[J].Nonlinear Dynamics,2012,67(2):1635-1646.
[8]苗中华,刘军,王国强,等.随机扰动下不确定网络化Euler-Lagrange系统的分群一致性[J].中国科学:信息科学,2016,46(11):1608-1620.
[9]ZHANG H,WU Q,JI J.Synchronization of discretely coupled harmonic oscillators using sampled position states only[J].IEEE Transactions on Automatic Control,2018,66(11):3994-3999.
[10]REN W.Synchronization of coupled harmonic oscillators with local interaction[J].Automatica,2008,44(12):3195-3200.
[11]BALLARD L,CAO Y,REN W.Distributed discrete-time coupled harmonic oscillators with application to synchronised motion coordination[J].IET Control Theory&Applications,2010,4(5):806-816.
[12]ZHANG H,JI J,WU Q.Sampled-data control of coupled harmonic oscillators using measured position states only[J].IET Control Theory&Applications,2018,12(7):985-991.
[13]ZHANG H,JI J.Group synchronization of coupled harmonic oscillators without velocity measurements[J].Nonlinear Dynamics,2018,91(6):2773-2788.
[14]万明非,张华,叶志勇,等.耦合调和振子网络系统的分群采样控制同步[J].重庆理工大学学报(自然科学),2018,32(3):242-248,272.
[15]SHANG Y.Synchronization in networks of coupled harmonic oscillators with stochastic perturbation and time delays[J].Mathematics&Its Applications Annals of the Academy of Romanian Scientists,2012,4(1):44-58.
[16]SUN W,YU X,LV J,et al.Synchronization of coupled harmonic oscillators with random noises[J].Nonlinear Dynamics,2015,79(1):473-484.
[17]GODSIL C,ROYLE G.Algebraic Graph Theory[M].New York:Springer-Verlag New York,2001.
[18]SU H,WANG X,LIN Z.Synchronization of coupled harmonic oscillators in a dynamic proximity network[J].Automatica,2009,45(10):2286-2291.
[19]MAO X,YUAN C.Stochastic differential equations with markovian switching[M].London:Imperial College Press,2006.
[20]OLFATI-SABER R,MURRAYR M.Consensus problems in networks of agents with switching topology and timedelays.IEEE Transactions on Automatic Control[J].2004,49(9):1520-1533.