基于混杂控制的复杂多智能体网络同步一致性研究
|
摘要
复杂网络是当前科学与工程领域的新兴学科,受到了国内外科研工作者的广泛关注。其中，同步和一致性是网络中两种典型的动力学行为,也是许多实际网络应用当中重要而又基本的问题。所以,它也是当今控制领域研究的热点与前沿。简单的说,同步和一致性问题主要是研究如何基于网络中节点与节点的局部信息交换来设计网络协调算法,使网络中所有的节点达到状态的趋同。本文在前人研究的基础上,利用稳定性理论、代数图论和混杂系统理论,系统深入的研究了复杂动态网络同步及多智能体网络一致性的混杂控制问题。全文主要内容概括如下：
研究了复杂网络的分布式脉冲同步问题。对于网络同步问题,前人提出过各种各样的控制策略,但大多数需要所有节点获得同样信息作为参考输入。而对于一个大型的网络系统来说,所有节点很难获得同样的信息。为了避免这种情况下的某些应用困难,引入了所谓控制拓扑的概念,用来描述整个网络的控制信息流。通过设计控制拓扑,来设计每个节点的控制器所使用的信息。基于控制拓扑的概念,提出了网络同步的分布式脉冲控制策略,并得到了复杂动态网络指数同步的充分条件。
在实际网络当中,时滞是经常出现的现象。忽略它的存在来进行分析,会产生错误的结论。针对时滞现象基于控制拓扑的概念,研究了含节点时滞和多重耦合时滞的复杂动态网络分布式脉冲同步。利用脉冲时滞系统的稳定性理论和比较原理,得到了一些网络指数同步的充分条件并给出了指数收敛率的上界。
针对多智能体网络,首先研究了一类一阶离散时间多智能体网络的分布式一致性问题。在其通讯模式中,每个时刻只有一个智能体随机的被选中，并通过量化通信对与其相邻的节点广播它的信息。对于这种通信方式,最基本的问题就是什么样的分布式的控制算法和什么样的网络结构一起作用,可以使网络达到一致。本文提出了一类广播gossip算法,并给出了关于网络拓扑结构的充分必要条件来确保网络达到量化一致。
针对二阶多智能体网络,研究了采样通信条件下连续时间二阶多智能体网络的分布式一致性问题。为了实现多智能休网络的一致,提出了两类脉冲一致性算法。这两种算法仅仅需要利用采样信息并且只在采样时刻运行。根据脉冲系统的稳定性理论与代数图论,得到了一些网络一致性的充分必要条件。研究发现控制增益、采样周期以及网络拉普拉斯矩阵的特征值在网络的一致性中都起着关键的作用。
针对有领航者的二阶智能体网络,通过脉冲一致性算法来使其达到一致。领航者是一类特殊的智能体,它的运动独立于其他所有的智能体,而且只有部分智能体能够获得领航者的信息。通过脉冲系统稳定性和非负矩阵理论,分别给出了固定拓扑下达到一致性的充分必要条件,和切换拓扑下的充分条件。
考虑了在切换拓扑和非均匀周期采样通讯下连续时间二阶多智能体网络的一致性问题。在系统中我们假设智能体无法获得任何关于速度的信息,它们只能使用相对位置信息。通过非负矩阵的相关理论,得到一些确保多智能体网络一致性的充分条件。当控制增益和非均匀采样周期满足某些条件时,如果网络的联合拓扑含有一个有向支撑树,则多智能体网络可以达到一致。
最后对全文进行了归纳总结,并对复杂多智能体网络的同步一致性问题的进一步研究和发展方向进行了展望。
Complex network is new and emerging scientific discipline that has drawn a great deal of attentions in recently years. In this field, synchronization and consensus of networks are important and essential problems for many network applications. Therefore, synchroniza-tion and consensus problem of networks is a focal and hot topic of great interest recently in control community. Roughly speaking, Synchronization and consensus is to design a network algorithm based on locally available information such that all nodes finally reach a state of agreement. This dissertation, based on previous works of the others, systemati-cally and deeply investigates the hybrid control for synchronization of complex dynamical networks and consensus of multi-agent systems. The main contents of this dissertation are outlined as follows.
The synchronization of complex dynamical networks is studied via impulsive control. Many control schemes were reported to achieve the network synchronization. In the most of the control schemes, all nodes should obtain the same information as control input. This may lead to the difficulty in some practical applications. Because it is not easy for all node to obtain the same information in a large scale network. In order to avoid above imple-mentation difficulty, the concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes, and the control topology can be designed according to different practical situations. Based on the control topology, the distributed impulsive control scheme is proposed to achieve the expo-nential synchronization of the network.
Complex dynamical networks with time delay are considered. It is noted that in the practical networks time delays are often encountered. Ignoring them may lead to design flaws and incorrect analysis conclusions. For time delay, based on the concept of control topology, the synchronization problem of the network with system delay and multiple cou-pling delays is studied via distributed impulsive control. By stability theory for impulsive delayed systems, some sufficient conditions for global exponential synchronization are de-rived, and moreover, the exponential convergence rate can be specified.
The distributed consensus problem of the first-order discrete-time multi-agent systems on directed networks are studied. For the communication of agents, it is assumed that only one agent can be selected with a prescribed probability and broadcasts its own state to neigh-bors via quantized communication (any arbitrary quantization) at each time step. For this kind of communication, the fundamental question is how to design distributed algorithms and what kinds of network topology that together lead to the quantized consensus. A class of broadcast gossip algorithms is proposed and a necessary and sufficient graphical condition is given to ensure the quantized consensus. In particular, the obtained graphical condition does not require symmetric network topology, which is weaker than those in some other literature. Several numerical simulations are given to show the effectiveness of the proposed algorithms.
The distributed consensus problem of the second-order continuous-time multi-agent networks with sampled-data communication are investigated. Motivated by the impulsive control strategy, two kinds of impulsive distributed algorithms are proposed for achieving consensus, These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, some necessary and sufficient conditions are obtained to ensure the con-sensus of the networks. It is shown that the control gains, the sampling size and the eigen-values of the Laplacian matrix of communication graph play key role in achieving the con-sensus.
The leader-following consensus problem of the multi-agent network is studied via the impulsive distributed algorithm. In the system, the agents only have local interaction and partial agents can obtain the information from the leader. Necessary and sufficient condition for fixed topology, and sufficient condition for switching topology are obtained.
The impulsive algorithm is proposed for consensus of the continuous-time second-order multi-agent system under switching topology with aperiodic sampled communication, when the agents are not able to obtain any information about velocity, but only position information. Some sufficient conditions are given to ensure consensus of the multi-agent system. When the conditions on the control gains and the time-varying sampling period are satisfied, the multi-agent system achieves consensus if the communication graph has a directed spanning tree jointly.
Finally, a summary has been done for all discussions in the dissertation. The research works further study are presented for the multi-agent networks.
研究了复杂网络的分布式脉冲同步问题。对于网络同步问题,前人提出过各种各样的控制策略,但大多数需要所有节点获得同样信息作为参考输入。而对于一个大型的网络系统来说,所有节点很难获得同样的信息。为了避免这种情况下的某些应用困难,引入了所谓控制拓扑的概念,用来描述整个网络的控制信息流。通过设计控制拓扑,来设计每个节点的控制器所使用的信息。基于控制拓扑的概念,提出了网络同步的分布式脉冲控制策略,并得到了复杂动态网络指数同步的充分条件。
在实际网络当中,时滞是经常出现的现象。忽略它的存在来进行分析,会产生错误的结论。针对时滞现象基于控制拓扑的概念,研究了含节点时滞和多重耦合时滞的复杂动态网络分布式脉冲同步。利用脉冲时滞系统的稳定性理论和比较原理,得到了一些网络指数同步的充分条件并给出了指数收敛率的上界。
针对多智能体网络,首先研究了一类一阶离散时间多智能体网络的分布式一致性问题。在其通讯模式中,每个时刻只有一个智能体随机的被选中，并通过量化通信对与其相邻的节点广播它的信息。对于这种通信方式,最基本的问题就是什么样的分布式的控制算法和什么样的网络结构一起作用,可以使网络达到一致。本文提出了一类广播gossip算法,并给出了关于网络拓扑结构的充分必要条件来确保网络达到量化一致。
针对二阶多智能体网络,研究了采样通信条件下连续时间二阶多智能体网络的分布式一致性问题。为了实现多智能休网络的一致,提出了两类脉冲一致性算法。这两种算法仅仅需要利用采样信息并且只在采样时刻运行。根据脉冲系统的稳定性理论与代数图论,得到了一些网络一致性的充分必要条件。研究发现控制增益、采样周期以及网络拉普拉斯矩阵的特征值在网络的一致性中都起着关键的作用。
针对有领航者的二阶智能体网络,通过脉冲一致性算法来使其达到一致。领航者是一类特殊的智能体,它的运动独立于其他所有的智能体,而且只有部分智能体能够获得领航者的信息。通过脉冲系统稳定性和非负矩阵理论,分别给出了固定拓扑下达到一致性的充分必要条件,和切换拓扑下的充分条件。
考虑了在切换拓扑和非均匀周期采样通讯下连续时间二阶多智能体网络的一致性问题。在系统中我们假设智能体无法获得任何关于速度的信息,它们只能使用相对位置信息。通过非负矩阵的相关理论,得到一些确保多智能体网络一致性的充分条件。当控制增益和非均匀采样周期满足某些条件时,如果网络的联合拓扑含有一个有向支撑树,则多智能体网络可以达到一致。
最后对全文进行了归纳总结,并对复杂多智能体网络的同步一致性问题的进一步研究和发展方向进行了展望。
Complex network is new and emerging scientific discipline that has drawn a great deal of attentions in recently years. In this field, synchronization and consensus of networks are important and essential problems for many network applications. Therefore, synchroniza-tion and consensus problem of networks is a focal and hot topic of great interest recently in control community. Roughly speaking, Synchronization and consensus is to design a network algorithm based on locally available information such that all nodes finally reach a state of agreement. This dissertation, based on previous works of the others, systemati-cally and deeply investigates the hybrid control for synchronization of complex dynamical networks and consensus of multi-agent systems. The main contents of this dissertation are outlined as follows.
The synchronization of complex dynamical networks is studied via impulsive control. Many control schemes were reported to achieve the network synchronization. In the most of the control schemes, all nodes should obtain the same information as control input. This may lead to the difficulty in some practical applications. Because it is not easy for all node to obtain the same information in a large scale network. In order to avoid above imple-mentation difficulty, the concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes, and the control topology can be designed according to different practical situations. Based on the control topology, the distributed impulsive control scheme is proposed to achieve the expo-nential synchronization of the network.
Complex dynamical networks with time delay are considered. It is noted that in the practical networks time delays are often encountered. Ignoring them may lead to design flaws and incorrect analysis conclusions. For time delay, based on the concept of control topology, the synchronization problem of the network with system delay and multiple cou-pling delays is studied via distributed impulsive control. By stability theory for impulsive delayed systems, some sufficient conditions for global exponential synchronization are de-rived, and moreover, the exponential convergence rate can be specified.
The distributed consensus problem of the first-order discrete-time multi-agent systems on directed networks are studied. For the communication of agents, it is assumed that only one agent can be selected with a prescribed probability and broadcasts its own state to neigh-bors via quantized communication (any arbitrary quantization) at each time step. For this kind of communication, the fundamental question is how to design distributed algorithms and what kinds of network topology that together lead to the quantized consensus. A class of broadcast gossip algorithms is proposed and a necessary and sufficient graphical condition is given to ensure the quantized consensus. In particular, the obtained graphical condition does not require symmetric network topology, which is weaker than those in some other literature. Several numerical simulations are given to show the effectiveness of the proposed algorithms.
The distributed consensus problem of the second-order continuous-time multi-agent networks with sampled-data communication are investigated. Motivated by the impulsive control strategy, two kinds of impulsive distributed algorithms are proposed for achieving consensus, These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, some necessary and sufficient conditions are obtained to ensure the con-sensus of the networks. It is shown that the control gains, the sampling size and the eigen-values of the Laplacian matrix of communication graph play key role in achieving the con-sensus.
The leader-following consensus problem of the multi-agent network is studied via the impulsive distributed algorithm. In the system, the agents only have local interaction and partial agents can obtain the information from the leader. Necessary and sufficient condition for fixed topology, and sufficient condition for switching topology are obtained.
The impulsive algorithm is proposed for consensus of the continuous-time second-order multi-agent system under switching topology with aperiodic sampled communication, when the agents are not able to obtain any information about velocity, but only position information. Some sufficient conditions are given to ensure consensus of the multi-agent system. When the conditions on the control gains and the time-varying sampling period are satisfied, the multi-agent system achieves consensus if the communication graph has a directed spanning tree jointly.
Finally, a summary has been done for all discussions in the dissertation. The research works further study are presented for the multi-agent networks.
引文
[1]Watts D, Strogatz S. Collective dynamics of'small-world'networks. Nature,1998, 393(6684):440-442.
[2]Barabasi A, Albert R. Emergence of scaling in random networks. Science,1999, 286(5439):509-512.
[3]Albert R, Barabasi A. Statistical mechanics of complex networks. Reviews of Modern Physics,2002,74(l):47-97.
[4]Newman M. The structure and function of complex networks. SIAM Review,2003, 45(2):167-256.
[5]Strogatz S. Exploring complex networks. Nature,2001,410(6825):268-276.
[6]Barabasi A, Oltvai Z. Network biology:Understanding the cell's functional organi-zation. Nature Reviews Genetics,2004,5(2):101-113.
[7]汪小帆,李翔,陈关荣.复杂网络理论及其应用.北京：清华大学出版社,2006.
[8]Bonabeau E, Dorigo M, Theraulaz G. Swarm intelligence:from natural to artificial systems. Oxford:Oxford University Press,1999.
[9]Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. PROCEEDINGS OF THE IEEE,2007,95(1):215-233.
[10]Arenas A, Diaz-Guilera A, Kurths J, et al. Synchronization in complex networks. Physics Reports,2008,469(3):95-153.
[11]Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans.on Automatic Control,2003,48(6):988-1001.
[12]Xiao L, Boyd S, Lall S. A scheme for robust distributed sensor fusion based on average consensus. in:Proceedings of 4th International Symposium on Information Processing in Sensor Networks, Boston, Massachusetts,2005,63-70.
[13]Kashyap A, Basar T, Srikant R. Quantized consensus. Automatica,2007, 43(7):1192-1203.
[14]Narendra K, Balakrishnan J. A common Lyapunov function for stable LTI sys-tems with commuting A-matrices. IEEE Transactions on Automatic Control,1994, 39(10):2469-2471.
[15]Branicky M. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control,1998,43(3):475-482.
[16]Hespanha J, Morse A. Stability of switched systems with average dwell-time. in: Proceedings of 38th IEEE Conference on Decision and Control, St. Louis, MO, USA, 1999,2655-2660.
[17]Lin H, Antsaklis P. Stability and Stabilizability of Switched Linear Systems:A Sur-vey of Recent Results. IEEE Transactions on Automatic Control,2009,54(2):308-322.
[18]Lakshmikantham V, Bainov D, Simeonov P. Theory of impulsive differential equa-tions. World Scientific Pub Co Inc,1989.
[19]Liu X, Ballinger G. Lyapunov conditions for input-to-state stability of impulsive systems. Computers and Mathematics with Applications,2001,41(7-8):903-915.
[20]Yang Z, Xu D. Stability analysis and design of impulsive control systems with time delay. IEEE Transactions on Automatic Control,2007,52(8):1448-1454.
[21]Chen W, Zheng W. Robust stability and H oo control of uncertain impulsive systems with time-delay. Automatica,2009,45(1):109-117.
[22]Zhang H, Guan Z H. Reliable dissipative control for stochastic impulsive systems. Automatica,2008,44(4):1004-1010.
[23]Hespanha J, Liberzon D, Teel A. Lyapunov conditions for input-to-state stability of impulsive systems. Automatica,2008,44(11):2735-2744.
[24]Guan Z, Liao R, Zhou F, et al. On impulsive control and its application to Chen's chaotic system. International Journal of Bifurcation and Chaos,2002,12(5):1191-1197.
[25]Guan Z, Chen G, Ueta T. On impulsive control of a periodically forced chaotic pendulum system. IEEE Transactions on Automatic Control,2000,45(9):1724-1727.
[26]Guan Z H, Hill D, Shen.X. Hybrid Impulsive and switching systems and applica-tion to control and synchronization. IEEE Transactions on Automatic Control,2005, 50(7):1448-1454.
[27]Guan Z, Hill D, Yao J. A hybrid impulsive and switching control strategy for synchro-nization of nonlinear systems and application to chua's chaotic circuit. International Journal of Bifurcation and Chaos,2006,16(1):229-238.
[28]Zheng S, Dong G, Bi Q. Impulsive synchronization of complex networks with non-delayed and delayed coupling. Physics Letters A,2009,373(46):4255-4259.
[29]Cai S, Zhou J, Xiang L, et al. Robust impulsive synchronization of complex delayed dynamical networks. Physics Letters A,2008,372(30):4990-4995.
[30]Neda Z, Ravasz E, Brechet Y, et al. Self-organizing processes:The sound of many hands clapping. Nature,2000,403(6772):849-850.
[31]Kaneko K. coupled map lattices. Chaos,1992,2(3):279-282.
[32]Wu C, Chua L. Synchronization in an array of linearly coupled dynamical systems. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, 1995,42(8):430-447.
[33]Pecora L, Carroll T. Master stability functions for synchronized coupled systems. Physical Review Letters,1998,80(10):2109-2112.
[34]Mou S, Gao H, Zhao Y, et al. Further improvement on synchronization stability of complex networks with coupling delays. International Journal of Computer Mathe-matics,2008,85(8):1255-1263.
[35]Wang Y, Wang Z, Liang J. A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Physics Letters A,2008, 372(39):6066-6073.
[36]Yuan K. Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing,2009,72(4-6):1026-1031.
[37]Yang M, Wang Y, Xiao J, et al. Robust synchronization of impulsively-coupled com-plex switched networks with parametric uncertainties and time-varying delays. Non-linear Analysis:Real World Applications,2010, 11(4):3008-3020.
[38]Wang Z, Wang Y, Liu Y. Global synchronization for discrete:time stochastic com-plex networks with randomly occurred nonlinearities and mixed time delays. IEEE Transactions on Neural Networks,2010,21(1):11-25.
[39]Yu W, Cao J, Lu J. Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J. Appl. Dyn. Syst,2008,7(1):108-133.
[40]Li C, Chen G. Synchronization in general complex dynamical networks with coupling delays. Physica A:Statistical Mechanics and its Applications,2004,343:263-278.
[41]Liu X, Chen T. Exponential synchronization of nonlinear coupled dynamical net-works with a delayed coupling. Physica A:Statistical Mechanics and its Applications, 2007,381:82-92.
[42]Liu T, Zhao J, Hill D. Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes. Chaos, Solitons & Fractals,2009,40(3):1506-1519.
[43]Zhou J, Chen T. Synchronization in general complex delayed dynamical networks. IEEE Transactions on Circuits and Systems I:Regular Papers,2006,53(3):733-744.
[44]Wang B, Guan Z. Chaos synchronization in general complex dynamical net-works with coupling delays. Nonlinear Analysis:Real World Applications,2010, 11 (3):1925-1932.
[45]Liu Y, Wang Z, Liang J, et al. Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,,2008,38(5):1314-1325.
[46]Gao H, Lam J, Chen G. New criteria for synchronization stability of general complex dynamical networks with coupling delays. Physics Letters A,2006,360(2):263-273.
[47]Papachristodoulou A, Jadbabaie A. Synchonization in oscillator networks with het-erogeneous delays, switching topologies and nonlinear dynamics. in:Proceedings of 45th IEEE Conference on Decision and Control. IEEE,2006,4307-4312.
[48]Tu L, Lu J. Delay-dependent synchronization in general complex delayed dynamical networks. Computers & Mathematics with Applications,2009,57(1):28-36.
[49]Yao J, Hill D, Guan Z, et al. Synchronization of complex dynamical networks with switching topology via adaptive control. in:Proceedings of 45th IEEE Conference on Decision and Control. IEEE,2006,2819-2824.
[50]Lu J, Chen G. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Transactions on Automatic Control,2005,50(6):841-846.
[51]Zhao J, Hill D, Liu T. Synchronization of complex dynamical networks with switch-ing topology:A switched system point of view. Automatica,2009,45(11):2502-2511.
[52]Stilwell D, Bollt E, Roberson D. Sufficient Conditions for Fast Switching Synchro-nization in Time-Varying Network Topologies. SIAM Journal on Applied Dynamical Systems,2006,5:140.
[53]Zhou C, Kurths J. Dynamical weights and enhanced synchronization in adaptive complex networks. Physical Review Letters,2006,96(16):164102.
[54]Zhou J, Lu J, Lu J. Pinning adaptive synchronization of a general complex dynamical network. Automatica,2008,44(4):996-1003.
[55]Zhou J, Lu J, Lu J. Adaptive synchronization of an uncertain complex dynamical network. IEEE Transactions on Automatic Control,2006,51(4):652-656.
[56]Sorrentino F, Ott E. Adaptive synchronization of dynamics on evolving complex networks. Physical review letters,2008,100(11):114101.
[57]Zhang Q, Lu J, Lu J, et al. Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Transactions on Circuits and Systems II:Express Briefs,2008,55(2):183-187.
[58]De Lellis P, Bernardo M, Garofalo F. Synchronization of complex networks through local adaptive coupling. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2008,18:037110.
[59]Lu W. Adaptive dynamical networks via neighborhood information:Synchronization and pinning control. Chaos:An Interdisciplinary Journal of Nonlinear Science,2007, 17:023122.
[60]DeLellis P, diBernardo M, Garofalo F. Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica,2009,45(5):1312-1318.
[61]Li X, Wang X, Chen G. Pinning a complex dynamical network to its equilibrium. IEEE Transactions on Circuits and Systems I:Regular Papers,2004,51(10):2074-2087.
[62]Yu W, Chen G, Lu J. On pinning synchronization of complex dynamical networks. Automatica,2009,45(2):429-435.
[63]Porfiri M, Bernardo M. Criteria for global pinning-controllabilily of complex net-works. Automatica,2008,44(12):3100-3106.
[64]Xiang J, Chen G. On the V-stability of complex dynamical networks. Automatica, 2007,43(6):1049-1057.
[65]Liu B, Liu X, Chen G, et al. Robust impulsive synchronization of uncertain dynam-ical networks. IEEE Transactions on Circuits and Systems Ⅰ:Regular Papers,2005, 52(7):1431-1441.
[66]Zhang G, Liu Z, Ma Z. Synchronization of complex dynamical networks via im-pulsive control. Chaos:An Interdisciplinary Journal of Nonlinear Science,2007, 17:043126.
[67]Olfati-Saber R, Fax J, Murray R. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE,2007,95(1):215-233.
[68]Tsitsiklis J, Athans M. On the complexity of decentralized decision making and detection problems. IEEE Transactions on Automatic Control,1985,30(5):440-446.
[69]Tsitsiklis J N. Problems in decentralized decision making and computation:[PhD Dissertation]. Boston:M. I. T., Dept. of Electrical Engineering and Computer Sci-ence,1984.
[70]Vicsek T, Czirok A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles. Physical Review Letters,1995,75(6):1226-1229.
[71]Xiao L, Boyd S. Fast linear iterations for distributed averaging. Systems & Control Letters,2004,53(1):65-78.
[72]Ren W, Beard R. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control,2005, 50(5):655-661.
[73]Moreau L. Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control,2005,50(2):169-182.
[74]Hatano Y, Mesbahi M. Agreement over random networks. IEEE Transactions on Automatic Control,2005,50(11):1867-1872.
[75]Tahbaz-Salehi A, Jadbabaie A. A necessary and sufficient condition for consensus over random networks. IEEE Transactions on Automatic Control,2008,53(3):791-795.
[76]Porfiri M, Stilwell D. Consensus seeking over random weighted directed graphs. IEEE Transactions on Automatic Control,2007,52(9):1767-1773.
[77]Xiao F, Wang L. Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays. IEEE Transactions on Automatic Control,2008,53(8):1804-1816.
[78]Carli R, Fagnani F, Frasca P, et al. Gossip consensus algorithms via quantized com-munication. Automatica,2010,46(1):70-80.
[79]Aysal T, Yildiz M, Sarwate A, et al. Broadcast algorithms for consensus. IEEE Transactions on Signal Processing,2009,57(7):2748-2761.
[80]Lin P, Jia Y, Li L. Distributed robust H∞ consensus control in directed networks of agents with time-delay. Systems & Control Letters,2008,57(8):643-653.
[81]Tian Y, Liu C. Consensus of multi-agent systems with diverse input and communica-tion delays. IEEE Transactions on Automatic Control,2008,53(9):2122-2128.
[82]Xiao F, Wang L. Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica,2008,44(10):2577-2582.
[83]Peng K, Yang Y. Leader-following consensus problem with a varying-velocity leader and time-varying delays. Physica A:Statistical Mechanics and its Applications,2009, 388(2-3):193-208.
[84]Hong Y, Hu J, Gao L. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica,2006,42(7):1177-1182.
[85]Cao Y, Ren W. Optimal linear-consensus algorithms:an LQR perspective. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,2010, 40(3):819-830.
[86]Huang M, Manton J. Coordination and consensus of networked agents with noisy measurements:Stochastic algorithms and asymptotic behavior. SIAM Journal on Control and Optimization,2009,48(1):134-161.
[87]Kar S, Moura J. Distributed consensus algorithms in sensor networks with imper-fect communication:Link failures and channel noise. IEEE Transactions on Signal Processing,2009,57(1):355-369.
[88]Li T, Zhang J. Mean square average-consensus under measurement noises and fixed topologies:Necessary and sufficient conditions. Automatica,2009,45(8):1929-1936.
[89]Li T, Zhang J. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Transactions on Automatic Control,2010,55(9):2043-2057.
[90]Nedic A, Olshevsky A, Ozdaglar A, et al. On distributed averaging algorithms and quantization effects. IEEE Transactions on Automatic Control,2009,54(11):2506-2517.
[91]Carli R, Bullo F, Zampieri S. Quantized average consensus via dynamic cod-ing/decoding schemes. International Journal of Robust and Nonlinear Control,2010, 20(2):156-175.
[92]Kar S, Moura J. Distributed consensus algorithms in sensor networks:Quantized data and random link failures. IEEE Transactions on Signal Processing,2010,58(3):1383-1400.
[93]Aysal T, Coates M, Rabbat M. Distributed average consensus with dithered quanti-zation. IEEE Transactions on Signal Processing,2008,56(10):4905-4918.
[94]Fagnani F, Zampieri S. Average consensus with packet drop communication. in: Proceedings of 45th IEEE Conference on Decision and Control,2009,1007-1012.
[95]Li T, Zhang J. Sampled-data based average consensus with measurement noises:con-vergence analysis and uncertainty principle. Science in China Series F:Information Sciences,2009,52(11):2089-2103.
[96]Cao Y, Ren W. Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting. International Journal of Robust and Nonlinear Control,2010,20(9):987-1000.
[97]Cao Y, Ren W. Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. International Journal of Control,2010,83(3):506-515.
[98]Gao Y, Wang L, Xie G, et al. Consensus of multi-agent systems based on sampled-data control. International Journal of Control,2009,82(12):2193-2205.
[99]Zhang Y, Tian Y. Consensus of Data-Sampled Multi-Agent Systems With Random Communication Delay and Packet Loss. IEEE Transactions on Automatic Control, 2010,55(4):939-943.
[100]Liu H, Xie G, Wang L. Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control. International Journal of Robust and Nonlinear Control,2010,20(15):1706-1722.
[101]Ren W, Atkins E. Distributed multi-vehicle coordinated control via local informa-tion exchange. International Journal of Robust and Nonlinear Control,2007,17(10-11):1002-1033.
[102]Yu W, Chen G, Cao M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica,2010,46(6):1089-1095.
[103]Lin P, Jia Y. Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica,2009, 45(9):2154-2158.
[104]Ren W, Moore K, Chen Y. High-order and model reference consensus algorithms in cooperative control of multivehicle systems. Journal of dynamic systems, measure-ment, and control,2007,129:678.
[105]Boyd S, Ghosh A, Prabhakar B, et al. Randomized gossip algorithms. IEEE Trans-actions on Information Theory,2006,52(6):2508-2530.
[106]Bullo F, Cortes J, Martinez S. Distributed control of robotic networks:a mathematical approach to motion coordination algorithms. Princeton:Princeton University Press, 2009.
[107]杨明,刘先忠.矩阵论.湖北武汉：华中科技大学出版社,2003.
[108]Li T, Fei S. Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays. Neurocomputing,2008,71(4-6):1069-1081.
[109]Li T, Fei S, Zhang K. Synchronization control of recurrent neural networks with distributed delays. Physica A:Statistical Mechanics and its Applications,2008, 387(4):982-996.
[110]Lu W, Chen T, Chen G. Synchronization analysis of linearly coupled systems de-scribed by differential equations with a coupling delay. Physica D:Nonlinear Phe-nomena,2006,221 (2):118-134.
[111]Wang Q, Duan Z, Chen G, et al. Synchronization in a class of weighted complex networks with coupling delays. Physica A:Statistical Mechanics and its Applications, 2008,387(22):5616-5622.
[112]Wen S, Chen S, Guo W. Adaptive global synchronization of a general complex dy-namical network with non-delayed and delayed coupling. Physics Letters A,2008, 372(42):6340-6346.
[113]Barahona M, Pecora L. Synchronization in small-world systems. Physical Review Letters,2002,89(5):54101.
[114]Chen T, Liu X, Lu W. Pinning complex networks by a single controller. IEEE Transactions on Circuits and Systems I:Regular Papers,2007,54(5):1317-1326.
[115]Lu H, Liu X, Lu W. Chaotic attractors in delayed neural networks. Phys. Lett. A, 2002,298:109-116.
[116]Newman M, Watts D. Renormalization group analysis of the small-world network model. Phys. Lett. A,1999,263:341-346.
[117]Lin Z, Francis B, Maggiore M. State agreement for continuous-time coupled nonlin-ear systems. SIAM Journal on Control and Optimization,2007,46(1):288-307.
[118]Guan Z, Ding L, Kong Z. Multi-radius geographical spatial networks:Statistical characteristics and application to wireless sensor networks. Physica A:Statistical Mechanics and its Applications,2010,389(1):198-204.
[119]Lavaei J, Murray R. On quantized consensus by means of gossip algorithm-Part I: Convergence proof. in:Proceedings of Proceedings of American Control Conference. IEEE,2009,394-401.
[120]黄琳.稳定性与鲁棒性的理论基础.北京：科学出版社,2003.
[121]Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following con-trol of multi-agent networks. Automatica,2008,44(3):846-850.
[122]Su H S, Wang X F, Lin Z L. Flocking of Multi-Agents With a Virtual Leader. IEEE Transactions On Automatic Control,2009,52(2):293-307.
[123]Zhu W, Cheng D. Leader-following consensus of second-order agents with multiple time-varying delays. Automatica,2010,46(12):1994-1999.
[124]Ren W. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control,2008,53(6):1503-1509.
[125]Gao Y, Wang L, Jia Y. Consensus of Multiple Second-Order Agents without Velocity Measurements. in:Proceedings of Proceedings of American Control Conference, St. Louis, MO, USA,2009,4464-4469.
[126]Yu W, Zheng W X, Chen G, et al. Second-order consensus in multi-agent dynam-ical systems with sampled position data. Automatica,2011, In Press. Doi:DOI: 10.1016/j.automatica.2011.02.027.
[2]Barabasi A, Albert R. Emergence of scaling in random networks. Science,1999, 286(5439):509-512.
[3]Albert R, Barabasi A. Statistical mechanics of complex networks. Reviews of Modern Physics,2002,74(l):47-97.
[4]Newman M. The structure and function of complex networks. SIAM Review,2003, 45(2):167-256.
[5]Strogatz S. Exploring complex networks. Nature,2001,410(6825):268-276.
[6]Barabasi A, Oltvai Z. Network biology:Understanding the cell's functional organi-zation. Nature Reviews Genetics,2004,5(2):101-113.
[7]汪小帆,李翔,陈关荣.复杂网络理论及其应用.北京：清华大学出版社,2006.
[8]Bonabeau E, Dorigo M, Theraulaz G. Swarm intelligence:from natural to artificial systems. Oxford:Oxford University Press,1999.
[9]Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. PROCEEDINGS OF THE IEEE,2007,95(1):215-233.
[10]Arenas A, Diaz-Guilera A, Kurths J, et al. Synchronization in complex networks. Physics Reports,2008,469(3):95-153.
[11]Jadbabaie A, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans.on Automatic Control,2003,48(6):988-1001.
[12]Xiao L, Boyd S, Lall S. A scheme for robust distributed sensor fusion based on average consensus. in:Proceedings of 4th International Symposium on Information Processing in Sensor Networks, Boston, Massachusetts,2005,63-70.
[13]Kashyap A, Basar T, Srikant R. Quantized consensus. Automatica,2007, 43(7):1192-1203.
[14]Narendra K, Balakrishnan J. A common Lyapunov function for stable LTI sys-tems with commuting A-matrices. IEEE Transactions on Automatic Control,1994, 39(10):2469-2471.
[15]Branicky M. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control,1998,43(3):475-482.
[16]Hespanha J, Morse A. Stability of switched systems with average dwell-time. in: Proceedings of 38th IEEE Conference on Decision and Control, St. Louis, MO, USA, 1999,2655-2660.
[17]Lin H, Antsaklis P. Stability and Stabilizability of Switched Linear Systems:A Sur-vey of Recent Results. IEEE Transactions on Automatic Control,2009,54(2):308-322.
[18]Lakshmikantham V, Bainov D, Simeonov P. Theory of impulsive differential equa-tions. World Scientific Pub Co Inc,1989.
[19]Liu X, Ballinger G. Lyapunov conditions for input-to-state stability of impulsive systems. Computers and Mathematics with Applications,2001,41(7-8):903-915.
[20]Yang Z, Xu D. Stability analysis and design of impulsive control systems with time delay. IEEE Transactions on Automatic Control,2007,52(8):1448-1454.
[21]Chen W, Zheng W. Robust stability and H oo control of uncertain impulsive systems with time-delay. Automatica,2009,45(1):109-117.
[22]Zhang H, Guan Z H. Reliable dissipative control for stochastic impulsive systems. Automatica,2008,44(4):1004-1010.
[23]Hespanha J, Liberzon D, Teel A. Lyapunov conditions for input-to-state stability of impulsive systems. Automatica,2008,44(11):2735-2744.
[24]Guan Z, Liao R, Zhou F, et al. On impulsive control and its application to Chen's chaotic system. International Journal of Bifurcation and Chaos,2002,12(5):1191-1197.
[25]Guan Z, Chen G, Ueta T. On impulsive control of a periodically forced chaotic pendulum system. IEEE Transactions on Automatic Control,2000,45(9):1724-1727.
[26]Guan Z H, Hill D, Shen.X. Hybrid Impulsive and switching systems and applica-tion to control and synchronization. IEEE Transactions on Automatic Control,2005, 50(7):1448-1454.
[27]Guan Z, Hill D, Yao J. A hybrid impulsive and switching control strategy for synchro-nization of nonlinear systems and application to chua's chaotic circuit. International Journal of Bifurcation and Chaos,2006,16(1):229-238.
[28]Zheng S, Dong G, Bi Q. Impulsive synchronization of complex networks with non-delayed and delayed coupling. Physics Letters A,2009,373(46):4255-4259.
[29]Cai S, Zhou J, Xiang L, et al. Robust impulsive synchronization of complex delayed dynamical networks. Physics Letters A,2008,372(30):4990-4995.
[30]Neda Z, Ravasz E, Brechet Y, et al. Self-organizing processes:The sound of many hands clapping. Nature,2000,403(6772):849-850.
[31]Kaneko K. coupled map lattices. Chaos,1992,2(3):279-282.
[32]Wu C, Chua L. Synchronization in an array of linearly coupled dynamical systems. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, 1995,42(8):430-447.
[33]Pecora L, Carroll T. Master stability functions for synchronized coupled systems. Physical Review Letters,1998,80(10):2109-2112.
[34]Mou S, Gao H, Zhao Y, et al. Further improvement on synchronization stability of complex networks with coupling delays. International Journal of Computer Mathe-matics,2008,85(8):1255-1263.
[35]Wang Y, Wang Z, Liang J. A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Physics Letters A,2008, 372(39):6066-6073.
[36]Yuan K. Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing,2009,72(4-6):1026-1031.
[37]Yang M, Wang Y, Xiao J, et al. Robust synchronization of impulsively-coupled com-plex switched networks with parametric uncertainties and time-varying delays. Non-linear Analysis:Real World Applications,2010, 11(4):3008-3020.
[38]Wang Z, Wang Y, Liu Y. Global synchronization for discrete:time stochastic com-plex networks with randomly occurred nonlinearities and mixed time delays. IEEE Transactions on Neural Networks,2010,21(1):11-25.
[39]Yu W, Cao J, Lu J. Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J. Appl. Dyn. Syst,2008,7(1):108-133.
[40]Li C, Chen G. Synchronization in general complex dynamical networks with coupling delays. Physica A:Statistical Mechanics and its Applications,2004,343:263-278.
[41]Liu X, Chen T. Exponential synchronization of nonlinear coupled dynamical net-works with a delayed coupling. Physica A:Statistical Mechanics and its Applications, 2007,381:82-92.
[42]Liu T, Zhao J, Hill D. Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes. Chaos, Solitons & Fractals,2009,40(3):1506-1519.
[43]Zhou J, Chen T. Synchronization in general complex delayed dynamical networks. IEEE Transactions on Circuits and Systems I:Regular Papers,2006,53(3):733-744.
[44]Wang B, Guan Z. Chaos synchronization in general complex dynamical net-works with coupling delays. Nonlinear Analysis:Real World Applications,2010, 11 (3):1925-1932.
[45]Liu Y, Wang Z, Liang J, et al. Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,,2008,38(5):1314-1325.
[46]Gao H, Lam J, Chen G. New criteria for synchronization stability of general complex dynamical networks with coupling delays. Physics Letters A,2006,360(2):263-273.
[47]Papachristodoulou A, Jadbabaie A. Synchonization in oscillator networks with het-erogeneous delays, switching topologies and nonlinear dynamics. in:Proceedings of 45th IEEE Conference on Decision and Control. IEEE,2006,4307-4312.
[48]Tu L, Lu J. Delay-dependent synchronization in general complex delayed dynamical networks. Computers & Mathematics with Applications,2009,57(1):28-36.
[49]Yao J, Hill D, Guan Z, et al. Synchronization of complex dynamical networks with switching topology via adaptive control. in:Proceedings of 45th IEEE Conference on Decision and Control. IEEE,2006,2819-2824.
[50]Lu J, Chen G. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Transactions on Automatic Control,2005,50(6):841-846.
[51]Zhao J, Hill D, Liu T. Synchronization of complex dynamical networks with switch-ing topology:A switched system point of view. Automatica,2009,45(11):2502-2511.
[52]Stilwell D, Bollt E, Roberson D. Sufficient Conditions for Fast Switching Synchro-nization in Time-Varying Network Topologies. SIAM Journal on Applied Dynamical Systems,2006,5:140.
[53]Zhou C, Kurths J. Dynamical weights and enhanced synchronization in adaptive complex networks. Physical Review Letters,2006,96(16):164102.
[54]Zhou J, Lu J, Lu J. Pinning adaptive synchronization of a general complex dynamical network. Automatica,2008,44(4):996-1003.
[55]Zhou J, Lu J, Lu J. Adaptive synchronization of an uncertain complex dynamical network. IEEE Transactions on Automatic Control,2006,51(4):652-656.
[56]Sorrentino F, Ott E. Adaptive synchronization of dynamics on evolving complex networks. Physical review letters,2008,100(11):114101.
[57]Zhang Q, Lu J, Lu J, et al. Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Transactions on Circuits and Systems II:Express Briefs,2008,55(2):183-187.
[58]De Lellis P, Bernardo M, Garofalo F. Synchronization of complex networks through local adaptive coupling. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2008,18:037110.
[59]Lu W. Adaptive dynamical networks via neighborhood information:Synchronization and pinning control. Chaos:An Interdisciplinary Journal of Nonlinear Science,2007, 17:023122.
[60]DeLellis P, diBernardo M, Garofalo F. Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica,2009,45(5):1312-1318.
[61]Li X, Wang X, Chen G. Pinning a complex dynamical network to its equilibrium. IEEE Transactions on Circuits and Systems I:Regular Papers,2004,51(10):2074-2087.
[62]Yu W, Chen G, Lu J. On pinning synchronization of complex dynamical networks. Automatica,2009,45(2):429-435.
[63]Porfiri M, Bernardo M. Criteria for global pinning-controllabilily of complex net-works. Automatica,2008,44(12):3100-3106.
[64]Xiang J, Chen G. On the V-stability of complex dynamical networks. Automatica, 2007,43(6):1049-1057.
[65]Liu B, Liu X, Chen G, et al. Robust impulsive synchronization of uncertain dynam-ical networks. IEEE Transactions on Circuits and Systems Ⅰ:Regular Papers,2005, 52(7):1431-1441.
[66]Zhang G, Liu Z, Ma Z. Synchronization of complex dynamical networks via im-pulsive control. Chaos:An Interdisciplinary Journal of Nonlinear Science,2007, 17:043126.
[67]Olfati-Saber R, Fax J, Murray R. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE,2007,95(1):215-233.
[68]Tsitsiklis J, Athans M. On the complexity of decentralized decision making and detection problems. IEEE Transactions on Automatic Control,1985,30(5):440-446.
[69]Tsitsiklis J N. Problems in decentralized decision making and computation:[PhD Dissertation]. Boston:M. I. T., Dept. of Electrical Engineering and Computer Sci-ence,1984.
[70]Vicsek T, Czirok A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles. Physical Review Letters,1995,75(6):1226-1229.
[71]Xiao L, Boyd S. Fast linear iterations for distributed averaging. Systems & Control Letters,2004,53(1):65-78.
[72]Ren W, Beard R. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control,2005, 50(5):655-661.
[73]Moreau L. Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control,2005,50(2):169-182.
[74]Hatano Y, Mesbahi M. Agreement over random networks. IEEE Transactions on Automatic Control,2005,50(11):1867-1872.
[75]Tahbaz-Salehi A, Jadbabaie A. A necessary and sufficient condition for consensus over random networks. IEEE Transactions on Automatic Control,2008,53(3):791-795.
[76]Porfiri M, Stilwell D. Consensus seeking over random weighted directed graphs. IEEE Transactions on Automatic Control,2007,52(9):1767-1773.
[77]Xiao F, Wang L. Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays. IEEE Transactions on Automatic Control,2008,53(8):1804-1816.
[78]Carli R, Fagnani F, Frasca P, et al. Gossip consensus algorithms via quantized com-munication. Automatica,2010,46(1):70-80.
[79]Aysal T, Yildiz M, Sarwate A, et al. Broadcast algorithms for consensus. IEEE Transactions on Signal Processing,2009,57(7):2748-2761.
[80]Lin P, Jia Y, Li L. Distributed robust H∞ consensus control in directed networks of agents with time-delay. Systems & Control Letters,2008,57(8):643-653.
[81]Tian Y, Liu C. Consensus of multi-agent systems with diverse input and communica-tion delays. IEEE Transactions on Automatic Control,2008,53(9):2122-2128.
[82]Xiao F, Wang L. Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica,2008,44(10):2577-2582.
[83]Peng K, Yang Y. Leader-following consensus problem with a varying-velocity leader and time-varying delays. Physica A:Statistical Mechanics and its Applications,2009, 388(2-3):193-208.
[84]Hong Y, Hu J, Gao L. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica,2006,42(7):1177-1182.
[85]Cao Y, Ren W. Optimal linear-consensus algorithms:an LQR perspective. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,2010, 40(3):819-830.
[86]Huang M, Manton J. Coordination and consensus of networked agents with noisy measurements:Stochastic algorithms and asymptotic behavior. SIAM Journal on Control and Optimization,2009,48(1):134-161.
[87]Kar S, Moura J. Distributed consensus algorithms in sensor networks with imper-fect communication:Link failures and channel noise. IEEE Transactions on Signal Processing,2009,57(1):355-369.
[88]Li T, Zhang J. Mean square average-consensus under measurement noises and fixed topologies:Necessary and sufficient conditions. Automatica,2009,45(8):1929-1936.
[89]Li T, Zhang J. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Transactions on Automatic Control,2010,55(9):2043-2057.
[90]Nedic A, Olshevsky A, Ozdaglar A, et al. On distributed averaging algorithms and quantization effects. IEEE Transactions on Automatic Control,2009,54(11):2506-2517.
[91]Carli R, Bullo F, Zampieri S. Quantized average consensus via dynamic cod-ing/decoding schemes. International Journal of Robust and Nonlinear Control,2010, 20(2):156-175.
[92]Kar S, Moura J. Distributed consensus algorithms in sensor networks:Quantized data and random link failures. IEEE Transactions on Signal Processing,2010,58(3):1383-1400.
[93]Aysal T, Coates M, Rabbat M. Distributed average consensus with dithered quanti-zation. IEEE Transactions on Signal Processing,2008,56(10):4905-4918.
[94]Fagnani F, Zampieri S. Average consensus with packet drop communication. in: Proceedings of 45th IEEE Conference on Decision and Control,2009,1007-1012.
[95]Li T, Zhang J. Sampled-data based average consensus with measurement noises:con-vergence analysis and uncertainty principle. Science in China Series F:Information Sciences,2009,52(11):2089-2103.
[96]Cao Y, Ren W. Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting. International Journal of Robust and Nonlinear Control,2010,20(9):987-1000.
[97]Cao Y, Ren W. Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. International Journal of Control,2010,83(3):506-515.
[98]Gao Y, Wang L, Xie G, et al. Consensus of multi-agent systems based on sampled-data control. International Journal of Control,2009,82(12):2193-2205.
[99]Zhang Y, Tian Y. Consensus of Data-Sampled Multi-Agent Systems With Random Communication Delay and Packet Loss. IEEE Transactions on Automatic Control, 2010,55(4):939-943.
[100]Liu H, Xie G, Wang L. Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control. International Journal of Robust and Nonlinear Control,2010,20(15):1706-1722.
[101]Ren W, Atkins E. Distributed multi-vehicle coordinated control via local informa-tion exchange. International Journal of Robust and Nonlinear Control,2007,17(10-11):1002-1033.
[102]Yu W, Chen G, Cao M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica,2010,46(6):1089-1095.
[103]Lin P, Jia Y. Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica,2009, 45(9):2154-2158.
[104]Ren W, Moore K, Chen Y. High-order and model reference consensus algorithms in cooperative control of multivehicle systems. Journal of dynamic systems, measure-ment, and control,2007,129:678.
[105]Boyd S, Ghosh A, Prabhakar B, et al. Randomized gossip algorithms. IEEE Trans-actions on Information Theory,2006,52(6):2508-2530.
[106]Bullo F, Cortes J, Martinez S. Distributed control of robotic networks:a mathematical approach to motion coordination algorithms. Princeton:Princeton University Press, 2009.
[107]杨明,刘先忠.矩阵论.湖北武汉：华中科技大学出版社,2003.
[108]Li T, Fei S. Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays. Neurocomputing,2008,71(4-6):1069-1081.
[109]Li T, Fei S, Zhang K. Synchronization control of recurrent neural networks with distributed delays. Physica A:Statistical Mechanics and its Applications,2008, 387(4):982-996.
[110]Lu W, Chen T, Chen G. Synchronization analysis of linearly coupled systems de-scribed by differential equations with a coupling delay. Physica D:Nonlinear Phe-nomena,2006,221 (2):118-134.
[111]Wang Q, Duan Z, Chen G, et al. Synchronization in a class of weighted complex networks with coupling delays. Physica A:Statistical Mechanics and its Applications, 2008,387(22):5616-5622.
[112]Wen S, Chen S, Guo W. Adaptive global synchronization of a general complex dy-namical network with non-delayed and delayed coupling. Physics Letters A,2008, 372(42):6340-6346.
[113]Barahona M, Pecora L. Synchronization in small-world systems. Physical Review Letters,2002,89(5):54101.
[114]Chen T, Liu X, Lu W. Pinning complex networks by a single controller. IEEE Transactions on Circuits and Systems I:Regular Papers,2007,54(5):1317-1326.
[115]Lu H, Liu X, Lu W. Chaotic attractors in delayed neural networks. Phys. Lett. A, 2002,298:109-116.
[116]Newman M, Watts D. Renormalization group analysis of the small-world network model. Phys. Lett. A,1999,263:341-346.
[117]Lin Z, Francis B, Maggiore M. State agreement for continuous-time coupled nonlin-ear systems. SIAM Journal on Control and Optimization,2007,46(1):288-307.
[118]Guan Z, Ding L, Kong Z. Multi-radius geographical spatial networks:Statistical characteristics and application to wireless sensor networks. Physica A:Statistical Mechanics and its Applications,2010,389(1):198-204.
[119]Lavaei J, Murray R. On quantized consensus by means of gossip algorithm-Part I: Convergence proof. in:Proceedings of Proceedings of American Control Conference. IEEE,2009,394-401.
[120]黄琳.稳定性与鲁棒性的理论基础.北京：科学出版社,2003.
[121]Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following con-trol of multi-agent networks. Automatica,2008,44(3):846-850.
[122]Su H S, Wang X F, Lin Z L. Flocking of Multi-Agents With a Virtual Leader. IEEE Transactions On Automatic Control,2009,52(2):293-307.
[123]Zhu W, Cheng D. Leader-following consensus of second-order agents with multiple time-varying delays. Automatica,2010,46(12):1994-1999.
[124]Ren W. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control,2008,53(6):1503-1509.
[125]Gao Y, Wang L, Jia Y. Consensus of Multiple Second-Order Agents without Velocity Measurements. in:Proceedings of Proceedings of American Control Conference, St. Louis, MO, USA,2009,4464-4469.
[126]Yu W, Zheng W X, Chen G, et al. Second-order consensus in multi-agent dynam-ical systems with sampled position data. Automatica,2011, In Press. Doi:DOI: 10.1016/j.automatica.2011.02.027.