通讯网络下群体的动力学行为
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摘要
本论文从系统控制学科的角度,运用图论、矩阵分析和现代控制理论等工具,研究通讯网络下群体的动力学行为。
我们考虑由多个具有相同动力学性质的个体组成的一类群体,其中每个个体如果不与其它个体发生作用的情况下是李亚普诺夫稳定的。当个体通过通讯网络采用分布式的线性控制协议的时候,我们分析、证明了群体在一个固定的通讯网络拓扑结构下的动力学行为,不仅和个体的动力学方程有关,而且和网络结构的代数特征有关。进一步,我们给出了群体出现渐近聚集、周期稳定和发散三种不同行为的条件。在网络存在时滞的情况下也得到类似结果。我们运用传递函数和线性矩阵不等式两种不同的控制理论方法分别给出常时滞和变时滞上界估计的具体算法。
在数字通讯网络的条件下,我们探讨了群体混合系统的动力学行为,证明了在信息采样周期和个体动力学反馈满足一定的条件下群体行为可能呈现聚集现象。当个体动力学反馈增益固定的时候,我们证明并且给出了存在唯一的信息采样周期使得群体达到临界周期稳定。同时,在信息采样周期固定的情况下,我们也证明并且给出了存在唯一的动力学反馈增益使得群体达到临界周期稳定。
最后,我们还用物理场论的方法建立了一类非线性群体动力学模型,表述个体间相互作用体现为远距离吸引,近距离排斥的特性,分析并且证明了在无向加权网络拓扑结构下群体将渐近地聚集到一个有界闭区域。在细节平衡(detailbalance)的有向强连通加权网络拓扑结构中,我们也得到类似结论。在数值仿真中,我们揭示了非线性群体不同的、多样性的聚集现象。进一步,我们还通过数值仿真探讨了在一般性的有向网络拓扑结构下的群体的动力学行为,展示了非线性模型中群体动力学行为的复杂性。
This thesis devotes to the study of dynamical behavior of multi-agent systems in network by the means of graph theory, matrix analysis, control theory and so on.
The multi-agent systems in network is a kind of swarms, which consists of many identical dynamical agents. The dynamics of each agent is Lyapunov stable when it is disconnected with other agents. We design a linear distributed protocol for the dynamical agents in communication network. When the communicated network is of fixed topology structure, we show that the dynamic behavior of swarms depends not only on the dynamical equations of agents, but also on the algebraic characteristic associated with the topology of the network. Moreover, we provide with the conditions under which the agents will gradually achieve aggregation, periodically stable or divergent trajectories. The similar results are extended to the case that the communication network is with transmission time-delay. The time-delay could be constant or time-varying. In this transmission time-delay case, we give in detail algorithms to estimate the upper bounds, for both cases: constant delays and time-varying delays, by means of transfer function and linear matrix inequality, respectively.
Under the condition of digital communicated network, we study the dynamic behavior of the swarms which is described by hybrid systems. It is shown that the behavior of the swarms will appear gradually aggregation if the sampling period and dynamic feedback of each agent are satisfied certain conditions. Fixing dynamic feedback gain, we show that there exists an unique sampling period such that the swarms achieve critical periodic stability. Moreover, if we fix sampling period, we also show that there exists an unique dynamic feedback gain such that the swarms achieve critical period stability.
Finally, we discuss the nonlinear swarm model where the interactions between any two agents are described by means of physical field. We use some nonlinear functions to define the interactions that governs a long range attraction and short range repulsion nature. It is shown that the members of swarms will asymptotically form a cohesive cluster with finite size if their communication network is an undirected weight topology structure. The similar results can be obtained under the condition that the topology structure of their communication network is a directed weight detailed balance. Meanwhile, we show that there exist various aggregation behaviors of swarms in nonlinear cases by numerical simulations.
Moreover, while the communication network of the agents is a directed weight topology structure, the dynamic behaviors of swarms are discussed by simulation examples. We show that the complex behaviors of swarms depend on the choices of the nonlinear attraction and repulsion functions in its mathematical models.
我们考虑由多个具有相同动力学性质的个体组成的一类群体,其中每个个体如果不与其它个体发生作用的情况下是李亚普诺夫稳定的。当个体通过通讯网络采用分布式的线性控制协议的时候,我们分析、证明了群体在一个固定的通讯网络拓扑结构下的动力学行为,不仅和个体的动力学方程有关,而且和网络结构的代数特征有关。进一步,我们给出了群体出现渐近聚集、周期稳定和发散三种不同行为的条件。在网络存在时滞的情况下也得到类似结果。我们运用传递函数和线性矩阵不等式两种不同的控制理论方法分别给出常时滞和变时滞上界估计的具体算法。
在数字通讯网络的条件下,我们探讨了群体混合系统的动力学行为,证明了在信息采样周期和个体动力学反馈满足一定的条件下群体行为可能呈现聚集现象。当个体动力学反馈增益固定的时候,我们证明并且给出了存在唯一的信息采样周期使得群体达到临界周期稳定。同时,在信息采样周期固定的情况下,我们也证明并且给出了存在唯一的动力学反馈增益使得群体达到临界周期稳定。
最后,我们还用物理场论的方法建立了一类非线性群体动力学模型,表述个体间相互作用体现为远距离吸引,近距离排斥的特性,分析并且证明了在无向加权网络拓扑结构下群体将渐近地聚集到一个有界闭区域。在细节平衡(detailbalance)的有向强连通加权网络拓扑结构中,我们也得到类似结论。在数值仿真中,我们揭示了非线性群体不同的、多样性的聚集现象。进一步,我们还通过数值仿真探讨了在一般性的有向网络拓扑结构下的群体的动力学行为,展示了非线性模型中群体动力学行为的复杂性。
This thesis devotes to the study of dynamical behavior of multi-agent systems in network by the means of graph theory, matrix analysis, control theory and so on.
The multi-agent systems in network is a kind of swarms, which consists of many identical dynamical agents. The dynamics of each agent is Lyapunov stable when it is disconnected with other agents. We design a linear distributed protocol for the dynamical agents in communication network. When the communicated network is of fixed topology structure, we show that the dynamic behavior of swarms depends not only on the dynamical equations of agents, but also on the algebraic characteristic associated with the topology of the network. Moreover, we provide with the conditions under which the agents will gradually achieve aggregation, periodically stable or divergent trajectories. The similar results are extended to the case that the communication network is with transmission time-delay. The time-delay could be constant or time-varying. In this transmission time-delay case, we give in detail algorithms to estimate the upper bounds, for both cases: constant delays and time-varying delays, by means of transfer function and linear matrix inequality, respectively.
Under the condition of digital communicated network, we study the dynamic behavior of the swarms which is described by hybrid systems. It is shown that the behavior of the swarms will appear gradually aggregation if the sampling period and dynamic feedback of each agent are satisfied certain conditions. Fixing dynamic feedback gain, we show that there exists an unique sampling period such that the swarms achieve critical periodic stability. Moreover, if we fix sampling period, we also show that there exists an unique dynamic feedback gain such that the swarms achieve critical period stability.
Finally, we discuss the nonlinear swarm model where the interactions between any two agents are described by means of physical field. We use some nonlinear functions to define the interactions that governs a long range attraction and short range repulsion nature. It is shown that the members of swarms will asymptotically form a cohesive cluster with finite size if their communication network is an undirected weight topology structure. The similar results can be obtained under the condition that the topology structure of their communication network is a directed weight detailed balance. Meanwhile, we show that there exist various aggregation behaviors of swarms in nonlinear cases by numerical simulations.
Moreover, while the communication network of the agents is a directed weight topology structure, the dynamic behaviors of swarms are discussed by simulation examples. We show that the complex behaviors of swarms depend on the choices of the nonlinear attraction and repulsion functions in its mathematical models.
引文
[1] Breder C. M., Equations Descriptive of Fish Schools and Other Animal Aggregations[J]. Ecology, Vol. 35, No. 3, 1954, pp. 361-370.
[2] Warburton K. and Lazarus J., Tendency-Distance Models of Social Cohesion in Animal Groups[J]. J. Theoretical Biol., Vol. 150, 1991, pp. 473-488.
[3] Partridge B. L., The Structure and Function of Fish Schools[J]. Sci. Amer., Vol. 245,1982, pp.114-123.
[4] Gueron S., Levin S. A., and Rubenstein D. I., The Dynamics of Herds: From Individuals to Aggregations[J]. J. Theoretical Biol., Vol. 182,1996, pp. 85-98.
[5] Mogilner A. and Edelstein-Keshet L., A Nonlocal Model For a Swarm[J]. J. Math. Biol., Vol.38, 1999, pp. 534-570.
[6] Gueron S. and Levin S. A., The Dynamics of Group Formation[J]. Math Biosci., Vol. 128, 1995, pp. 243-264.
[7] Parrish J. K. and Haniner W. M., Eds., Animal Groups in Three Dimensions[M]. Cambridge, U.K.: Cambridge University Press, 1997.
[8] Camazine S., Deneubourg J.-L., Franks N. R.,Sneyd J., Theraulaz G. and Bonabeau E., Self-Organization in Biological Systems[M]. Princeton, NJ: Princeton Univ. Press, Apr. 2001.
[9] Hubbard S., Babak P., Sigurdsson S. T. and Magnusson K. G., A Model of the formation of fish schools and migrations of fish[J]. Ecological Modelling, Vol. 174, No.4, 2004, pp. 359-374.
[10] Parrish J.K., Viscido S. V., and Grvnbaum D., Self-Organized Fish School: an Examination of Emergent Properties[J]. Biol. Bull., Vol. 202, 2002, pp. 296-305.
[11] Grvnbaum D., Schooling As a Strategy For Taxis In a Noisy Environment[J]. Evolutionary Ecol., Vol. 12, 1998, pp. 503-522.
[12] Okubo A., Dynamical Aspects of Animal Grouping: Swarms, Schools, Flocks, and Herds[J]. Adv. Biophys., vol. 22,1986, pp. 1-94.
[13] Edelstein-Keshet L., Mathematical Models in Biology[J]. New York: Random House, 1989.
[14] Murray J. D., Mathematical Biology. New York: Springer-Verlag, 1989.
[15] Grvnbaum D. and Okubo A., Modeling Social Animal Aggregations[J]. in Frontiers in Theoretical Biology. New York: Springer-Verlag, Vol. 100,1994, pp. 296-325.
[16] Toner J. and Tu Y., Flochs, Herds, and Schools: a Quantitative Theory of Flocking[J]. Phys. Rev. E, Vol. 58, No.4,1998, pp.4828-4858.
[17] Bonabeau E., Dorigo M., and Theraulaz G., Swarm Intelligence: From Natural to Artificial Systems[M]. New York: Oxford Univ. Press, 1999.
[18] Giulietti F., Pollini L. and Innocenti M., Autonomous Formation Flight[J]. IEEE Control Syst. Mag., Vol. 20, No. 10, 2000, pp. 34-44.
[19] Burgard W., Moors M., Stachniss C. and Schneider F. E., Coordinated Multi-Robot Ex-ploration[J]. IEEE Transactions on Robotics, Vol.21, No.3,2005,pp.376-386.
[20] Ahmad R., Lee Yung-Chuan, Rahimi S., Gupta B., A Multi-Agent Based Approach for Particle Swarm Optimization[C]. Integration of Knowledge Intensive Multi-Agent Systems, 2007. KIMAS 2007. International Conference on April 30 2007, pp. 267-271.
[21] Mazurowski M.A. and Zurada J.M., Solving Multi-agent Control Problems Using Particle Swarm Optimization[C]. Swarm Intelligence Symposium, 2007. SIS 2007. IEEE 1-5 April 2007 pp. 105-111
[22] Balch T. and Arkin R. C., Behavior-Based Formation Control for Multirobot Teams[J]. IEEE Trans. Robot. Automat., Vol. 14, No. 12, 1998, pp. 926-939.
[23] Suzuki I. and Yamashita M., Distributed Anonymous Mobile Robots: Formation of Geometric Patterns[J]. SIAM J. Comput., Vol. 28, No. 4, 1999, pp. 1347-1363.
[24] Yamaguchi H., A Cooperative Hunting Behavior by Mobile-Robot Troops[J]. Int. J. Robot. Res., Vol.18, Sept. 1999, pp. 931-940.
[25] Maurizio Porfiri, Roberson D. Gray and Stilwell Daniel J., Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach[J]. Automatica Vol.43, 2007, pp. 1318-1328.
[26] Jongeun Choi, Joonho Lee, Songhwai Oh, Biologically-Inspired Navigation Strategies for Swarm Intelligence Using Spatial Gaussian Processes[C]. To be appeared in the 17th International Federation of Automatic Control(2008.7).
[27] Tanner H. G., Pappas G. J., Kumar V., Leader-to-Formation Stability[J]. IEEE Trans. Autom. Robot., Vol.20, No.3,2004, PP. 443-455.
[28] Lafferriere G, Williams A, Caughman J, Veerman JJP. Decentralized Control of Vehicle Formations[J]. Systems and Control Letters, Vol.54, No.9,2005, pp. 899-910.
[29] Lin Zhiyun, Bruce Francis and Manfredi Maggiore, Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles[J]. IEEE Trans. Automat. Control, Vol.50, No.l,2005,pp.l21-127.
[30] Bulentozguler A., Global Stabiliztion Via Local Stabilizing Actions[J]. IEEE Trans. Automat. Control,Vol.51, No.3,2006, PP.530-533.
[31] Reif J. H. and Wang H., Social Potential Fields: a Distributed Behavioral Control for Autonomous Robots[J]. Robot. Auton. Syst., Vol. 27, 1999, pp. 171-194.
[32] Desai J. P., Ostrowski J. and Kumar V, Controlling Formations of Multiple Mobile Robots[C]. in Proc. IEEE Int. Conf. Robot. Automat., Leuven, Belgium, May 1998, pp. 2864-2869.
[33] Egerstedt M. and Hu X., Formation Constrained Multi-Agent Control[J]. IEEE Trans Robot. Automat., Vol. 17, Dec. 2001, pp. 947-951.
[34] Reynolds C. W., Flocks, Birds, and Schools: A Distributed Behavioral Model[J]. Comput. Graph., Vol.21, 1987, pp. 25-34.
[35] Vicsek X, Czirok A., Ben-Jacob E., Cohen I. and Shochet O., Novel Type of Phase Transition in a System of Self-Driven Particles[J]. Phys. Rev. Lett., Vol. 75, No. 6, 1995, pp. 1226-1229.
[36] Czirok A., Ben-Jacob E., Cohen I., and Vicsek T., Formation of Complex Bacterial Colonies Via Self-Generated Vortices[J]. Phys. Rev. E., Vol. 54, No. 2, 1996, pp. 1791-1801.
[37] Czirok A., Stanley H. E., and Vicsek T., Spontaneously Ordered Motion of Self-propelled Particles[J]. J. Phys. A: Math Nucl. General, Vol. 30, 1997, pp. 1375-1385.
[38] Czirok A. and Vicsek T., Collective Behavior of Interacting Self-Propelled Particles[J]. Physica A, Vol. 281,2000, pp. 17-29.
[39] Shimoyama N., Sugawa K., Mizuguchi T., Hayakawa Y., and Sano M., Collective Motion in a System of Motile Elements[J]. Phys. Rev. Lett., Vol. 76, No. 20,1996, pp. 3870-3873.
[40] Levine H. and Rappel W.-J., Self-Organization in Systems of Self-Propelled Particles[J]. Phys. Rev. E, Vol. 63, No. 1, January 2001, pp. 017 101-1-017 101-4.
[41] Fax J. A. and Murray R. M., Information Flow and Cooperative Control of Vehicle For-mations[J]. IEEE Trans. Automat. Control, Vol.49, No.9,2004, pp. 1465-1476.
[42] Jadbabaie A., Lin J.and Morse S. A., Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules[J]. IEEE Trans. Automat. Control, Vol.48, No.6, 2003, pp. 988-1000.
[43] Moshtagh N. and Jadbabaie A., Distributed Geodesic Control Laws for Flocking of Non-holonomic Agents[J]. IEEE Trans. Automat. Control, Vol.52, No.4, 2007, pp. 681-686.
[44] S. Prajna, A. Jadbabaie, G. J. Pappas, A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates[J]. IEEE Trans. Automat. Control, Vol.52, No.8, 2007, pp. 1415-1428.
[45] Tanner H. G., Jadbabaie A. and Pappas G. J., Flocking in Fixed and Switching Net-works[J]. IEEE Trans. Automat. Control, Vol.52, No.5, 2007, pp. 863-868.
[46] Tsitsiklis J. N. and Bertsekas D. P.. Comment on Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules[J]. IEEE Trans. Automat. Control, Vol. 52, No. 5, 2007, pp. 968-969.
[47] Ren W. and Beard R. W., Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies[J]. IEEE Trans. Automat. Control,, Vol.50,2005, pp.655-661.
[48] Saber, R.O. and Murray, R.M., Consensus Problems in Networks of Agents with Switching Topology and Time-Delays[J]. IEEE Trans. Automat. Control, Vol.49, No.9,2004, pp. 1520-1533.
[49] Saber R.O., Fax J. A. and Murray R.M., Consensus and Cooperation in Networked Multiagent Systems[J]. Proceedings of the IEEE,, Vol.95, No.1, 2007, pp. 215-240.
[50] Fang L., Antsaklis P. J., and Tzimas A., Asynchronous Consensus Protocols: Preliminary Results, Simulations and Open Questions[C]. in 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC ' 05), Dec. 2005, pp. 2194-2199.
[51] Dimarogonas D. V. and Kyriakopoulos K. J., Formation Control and Collision Avoidance for Multi-Agent Systems and a Connection between Formation Infeasibility and Flocking Behavior[C]. in 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC ' 05), Dec. 2005, pp. 84-89.
[52] Lin Z., Brouke M., and Francis B., Local Control Strategies for Groups of Mobile Autonomous Agents[J]. IEEE Trans. Autom. Control, Vol.49, No.4, 2004, pp. 622-629.
[53] Moreau L., Stability of Multiagent Systems with Time-Dependent Communication[J]. IEEE Trans. Automat. Control, Vol.50, No.l, 2005, pp. 169-182.
[54] Olfati-Saber R., Ultrafast Consensus in Small-World Networks[C]. ACC, 2005, pp. 2371-2378.
[55] Cortes J., Achieving Coordination Tasks in Finite Time Via Nonsmooth Gradient-flows[C]. in Proc. 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC '05), Dec. 2005, pp. 6376-6381.
[56] Olfati-Saber R., Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory[J]. IEEE Trans. Autom. Control, Vol. 51, No. 3, 2006, pp. 401-420.
[57] Lin Z., Francis B., and Maggiore M., State Agreement for Continuous-Time Coupled Nonlinear Systems[J]. SIAM Journal on Control and Optimization, Vol.46, No.l, 2007, pp.288-307.
[58] Xiao L. and Boyd S., Fast Linear Iterations for Distributed Averaging[J]. Systems and Control Letters, Vol. 53, 2005, pp. 65-78.
[59] Angeli D. and Bliman P. A., Stability of Leaderless Discrete-Time Multi-Agent Sys-tems[J]. Mathematics of Control, Signals, and Systems, Vol.18, 2006, pp. 293-322.
[60] Hayashi N., Ushio T., Harada F. and Ohno A., Consensus Problem of Multi-Agent Systems with Nonlinear Performance Functions[C].IEICE Fundamentals, E90-A 2007(10), pp. 2261-2264.
[61] Bauso D., Giarre L., and Pesenti R., Nonlinear Protocols for Optimal Distributed Consensus in Networks of Dynamic Agents[J]. Systems and Control Letters, Vol. 55, No.11, 2006, pp.918-928.
[62] Albert B. and Barabasi A.-L., Statistical Mechanics of Complex Networks[J]. Reviews of Modern Physics, Vol.74, 2002, pp. 47-97.
[63] Hatano Y. and Mesbahi M., Agreement Over Random Networks[J]. IEEE Trans. Autom. Control, Vol. 50, No. 11,2005, pp. 1867-1872.
[64] Blondel V. D., Hendrickx J. M., Olshevsky A. and Tsitsiklis J. N.. Convergence in Mul-tiagent Coordination, Consensus, and Flocking[C]. Proceedings of the Joint 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain. 2005.
[65] Gazi V. and Passino K. M., Stability Analysis of Swarms[J]. IEEE Trans. Automat. Contr., Vol.48, No.4,2003, pp. 692-697.
[66] Gazi V. and Passion K.M., Stability Analysis of Social Foraging Swarms[J]. IEEE Trans. System, man and Cybernetics-B, Vol.34, No.1, 2004, pp.539-557.
[67] Gazi V. and Passino K.M., Stability of a One-Dimensional Discrete-Time Asynchronous Swarm[J]. Systems, Man and Cybernetics, Part B, IEEE Transactions on Volume 35, Issue 4,Aug.2005,pp.834-841.
[68] Gazi V, Swarm Aggregations Using Artificial Potentials and Sliding-mode Control[J]. Robotics, IEEE Transactions on [see also Robotics and Automation, IEEE Transactions on], Vol. 21, Issue 6, Dec. 2005, pp. 1208-1214.
[69]Gazi V.,Stability of an Asynchronous Swarm With Time-Dependent Communication Links[J].Systems,Man,and Cybernetics,Part B,IEEE Transactions on,Vol.38,Issue 1,Feb.2008,pp.267-274.
[70]Liu Y.and Passino K.M.,Stable Social Foraging Swarms in a Noisy Environment[J].IEEE Trans.Automat.Control,Vol.49,No.1,2004,pp.30-44.
[71]Liu Y.and Passino K.M.,Cohesive Behaviors of Multiagent Systems With Information Flow Constraints[J].Automatic Control,IEEE Transactions on,Vol.51,Issue 11,Nov.2006,pp.1734-1748.
[72]Savkin,A.V.,Coordinate Collective Motion of Groups of Autonomous Mobile Robots:Analysis of Vicsek's Model[J].IEEE Trans.Automat.Control,Vol.49,No.6,2004,pp.981-983.
[73]Liu Y.,Passino K.M.and Polycarpou M.M.,Stability Analysis of One-Dimensional Asynchronous Swarms[J].IEEE Transactions on Automatic Control,Vol.48,No.10,2003,pp.1848-1854.
[74]Savkin A.V.,Coordinated Collective Motion of Groups of Autonomous Mobile Robots:Analysis of Vicsek' s Model[J].IEEE Trans.Autom.Contr.,Vol.49,No.6,2004,pp.981-983.
[75]Liu Y.,Passino K.M.and Polycarpou M.,Stability Analysis of m-Dimensional Asynchronous Swarms with a Fixed Communication Topology[J].IEEE Trans.Automat.Contr.,Vol.48,No.1,2003,pp.76-95.
[76]程代展,陈翰馥.从群集到社会行为控制[J].科技导报,No.8,2005,pp.4-7.
[77]Guo L.,Liu Z.and Han J.,Multi-Agent Systems with Local Rules:Towards a Theory of Analysis and Control[C].Chinese Contr.Conf.,43,2006.
[78]楚天广,陈志绣,王龙,谢广明.群体动力学与协调控制[C].第二十六届中国控制会议论文集,2007.
[79]Chen Z.and Chu T.,Aggregation and Pattern Formation of Multi-Agent System[J].Chinese Contr.Conf.,2007,pp.26-31.
[80] Shi H., Wang L. and Chu T., Swarming Behavior of Multiagent Systems[J]. J. Contr. Theory Appl., Vol.2, No.4,2004, pp.313-318.
[81] B. Liu, T. Chu, L. Wang, Z. Wang, Swarm dynamics of a group of mobile autonomous agents[J]. Chinese Phys. Lett., Vol.22, 2005, pp. 254-257.
[82] Liu, Bo; Xie, Guangming; Chu, Tianguang; Wang, Long, Controllability of Interconnected Systems via Switching Networks with a Leader Systems[C]. Man and Cybernetics, 2006. ICSMC '06. IEEE International Conference on Volume 5, 8-11 Oct. 2006 pp.3912-3916.
[83] Leng Cuiping, Zheng Yufan and Yu Hongwang, A Formation Control for Dynamical Agents in Digital Network[C].The 6th International Conference on Control and Automation (IEEE ICCA), 2007.5.
[84] Chu T., Wang L., Chen T. and Mu S., Self-Organized Motion in a Class of Anisotropic Swarms: Convergence vs Oscillation[J]. Chaos, Solitons Fractals, Vol.30, 2006, pp.875-885.
[85] Mu S., Chu T. and Wang L., Coordinated Collective Motion in a Motile Particle Group With a Leader[J]. Physica A, Vol.351,2005, pp.211-226.
[86] Shi H., Wang L. and Chu T., Virtual Leader Approach to Coordinated Control of Multiple Mobile Agents with Asymmetric Interactions[J]. Physica D, Vol.213, 2006, pp.51-65.
[87] Hong Y., Gao L., Cheng D. and J. Hu, Lyapunov-Based Approach to Multiagent Systems with Switching Jointly Connected Interconnection[J]. IEEE Trans. Autom. Contr., Vol.52, No.5, 2007,pp.943-948.
[88] Jiangping Hu and Yiguang Hong, Leader-Following Coordination of Multi-Agent Systems with Coupling Time Delays[J]. Physica A, Vol.374, 2007, pp. 853-863.
[89] Xiao F., Wang L. and Wang A., Consensus Problems in Discrete-Time Multiagent Systems with Fixed Topology[J]. J. Math. Anal. Appl., Vol.322, No.2, 2006, 587-598.
[90] Sun Yuan Gong, Wang Long and Xie Guangming, Average Consensus in Directed Networks of Dynamic Agents with Time-Varying Communication Delays[C].Decision and Control, 2006 45th IEEE Conference on 13-15 Dec. 2006, pp.3393-3398.
[91] Sun Yuan Gong, Wang Long and Xie Guangming, Average Consensus in Networks of Dynamic Agents with Switching Topologies and Multiple Time-Varying Delays[J]. Systems and Control Letters, Vol.57,No.2, 2008, pp: 175-183.
[92] Bliman P. A. and Ferrari-Trecate G., Average Consensus Problems in Networks of Agents with Delayed Communications[C]. Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on 12-15, Dec. 2005,pp.7066-7071.
[93] Lee Dongjun and Spong Mark W., Agreement with Non-Uniform Information Delays[C]. Proceedings of the 2006 American Control Conference, 2006, pp. 756-761.
[94] Gu Dongbing, Distributed Particle Filter for Target Tracking[C]. Robotics and Automation, 2007 IEEE International Conference on 10-14, April 2007, pp.3856-3861.
[95] Jin Zhipu and Murray Richard M, Random Consensus Protocol in Large-Scale Net-works[C]. Decision and Control, 2007 46th IEEE Conference on 12-14, Dec. 2007, pp.4227-4232.
[96] Chen Jen-Yeu and Hu Jianghai, On the Convergence of Distributed Random Grouping for Average Consensus on Sensor Networks with Time-Varying Graphs[C]. Decision and Control, 2007 46th IEEE Conference on 12-14, Dec. 2007 pp.4233-4238.
[97] Xiao F. and Wang L., State Consensus for Multi-Agent Systems with Switching Topologies and Time-Varying Delays[J]. Int. J. Control, Vol.79, No. 10, 2006, pp. 1277-1284.
[98] Xiao F. and Wang L., Dynamic Behavior of Discrete-Time Multiagent Systems with General Communication Structures[J]. Physica A, Vol.370, No.2, 2006, pp.364-380.
[99] Xiao Feng, Wang Long and Jia Yingmin, Fast Information Sharing in Networks of Autonomous Agents. To be appeared in American Control Conference(2008).
[100] Liu Y., Jia Y., Du J. and Yu F., Average-Consensus Problems in Multiagent Sys-tems[C].European Control Conference, 2007.
[101] Chu T., Wang L. and Chen T., Self-Organized Motion in a Class of Anisotropic Swarms: Convergence vs Oscillation[C]. Proceedings of American Control Conference, 8-10 June 2005 ,vol. 5, 2005, pp.3474-3479.
[102] Lin Peng, Jia Yingmin, Average Consensus in Networks of Multi-Agents with Both Switching Topology and Coupling Time-Delay[J]. Physica A, Vol.387,2008, pp. 303-313.
[103] Xie Guangming and Wang Long, Consensus Control for a class of Networks of Dynamic Agents[J]. Int. J. of Robust and Nonlinear Control, Vol.17, 2007, pp.941-959.
[104] Hong Y., Hua J. and Gao L., Tracking Control for Multi-Agent Consensus with an Active Leader and Variable Topology[J]. Automatica, Vol.42, 2006, pp. 1177-1182.
[105] Maurizio Porfiri and Daniel J. Stilwell, Consensus Seeking Over Random Weighted Directed Graphs[J]. IEEE Trans. Autom. Control, Vol. 52, No. 9, Dec. 2007, pp. 1767-11773.
[106] Kar S., Moura J. M. F., Distributed Average Consensus in Sensor Networks with Random Link Failures[C]. Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on Volume 2, 15-20 April 2007, pp.II-1013-II-1016.
[107] Patterson Stacy , Bamieh Bassam and El Abbadi Amr, Distributed Average Consensus with Stochastic Communication Failures[C]. Decision and Control, 2007 46th IEEE Conference on 12-14 Dec. 2007, pp.4215-4220.
[108] Fagnani F. and Zampieri S., Randomized Consensus Algorithms Over Large Scale Net-works[C]. Information Theory and Applications Workshop, 2007 Jan. 29 2007-Feb. 2 2007, pp. 150-159.
[109] Tahbaz-Salehi A. and Jadbabaie A., On Consensus in Random Networks[C]. Allerton Conference on Communication, Control, and Computing, Allerton House IL, 2007.
[110] David Angeli and Pierre-Alexandre Bliman, Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees[J]. arXiv: math/0610854v1, 2007.
[111] Fiedler M., Algebraic Connectivity of Graphs[J]. Czechoslovak Math. J., Vol. 23, No. 98, 1973, pp. 298-305.
[112] Merris R., Laplacian Matrices of a Graph: A Survey[J]. Linear Algebra its Appl., Vol. 197, 1994, pp. 143-176.
[113] Biggs N., Algebraic, Graph Theory[M]. Cambridge University Press, Combridge, 1994.
[114]Hom R.A.and Johnson C.R.,Matrix Analysis[M].Cambridge,U.K.:Cambridge Univ.Press,1987.
[115]郑大钟,《线性系统理论》[M].北京:清华大学出版社,2002.
[116]黄琳,稳定性与鲁棒性的理论基础[M].北京:科学出版社,2003.
[117]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用[M].北京:清华大学出版社,2003
[118]Isidori A.,Nonlinear Control Systems Ⅱ[M].Communications and Control Engineering Series.Springer-Vedag,London,1999.
[119]Khalil H.K.,Nonlinear Systems(2nd ed.)[M].Upper Saddle River,N J:Prentice-Hall,1996.
[2] Warburton K. and Lazarus J., Tendency-Distance Models of Social Cohesion in Animal Groups[J]. J. Theoretical Biol., Vol. 150, 1991, pp. 473-488.
[3] Partridge B. L., The Structure and Function of Fish Schools[J]. Sci. Amer., Vol. 245,1982, pp.114-123.
[4] Gueron S., Levin S. A., and Rubenstein D. I., The Dynamics of Herds: From Individuals to Aggregations[J]. J. Theoretical Biol., Vol. 182,1996, pp. 85-98.
[5] Mogilner A. and Edelstein-Keshet L., A Nonlocal Model For a Swarm[J]. J. Math. Biol., Vol.38, 1999, pp. 534-570.
[6] Gueron S. and Levin S. A., The Dynamics of Group Formation[J]. Math Biosci., Vol. 128, 1995, pp. 243-264.
[7] Parrish J. K. and Haniner W. M., Eds., Animal Groups in Three Dimensions[M]. Cambridge, U.K.: Cambridge University Press, 1997.
[8] Camazine S., Deneubourg J.-L., Franks N. R.,Sneyd J., Theraulaz G. and Bonabeau E., Self-Organization in Biological Systems[M]. Princeton, NJ: Princeton Univ. Press, Apr. 2001.
[9] Hubbard S., Babak P., Sigurdsson S. T. and Magnusson K. G., A Model of the formation of fish schools and migrations of fish[J]. Ecological Modelling, Vol. 174, No.4, 2004, pp. 359-374.
[10] Parrish J.K., Viscido S. V., and Grvnbaum D., Self-Organized Fish School: an Examination of Emergent Properties[J]. Biol. Bull., Vol. 202, 2002, pp. 296-305.
[11] Grvnbaum D., Schooling As a Strategy For Taxis In a Noisy Environment[J]. Evolutionary Ecol., Vol. 12, 1998, pp. 503-522.
[12] Okubo A., Dynamical Aspects of Animal Grouping: Swarms, Schools, Flocks, and Herds[J]. Adv. Biophys., vol. 22,1986, pp. 1-94.
[13] Edelstein-Keshet L., Mathematical Models in Biology[J]. New York: Random House, 1989.
[14] Murray J. D., Mathematical Biology. New York: Springer-Verlag, 1989.
[15] Grvnbaum D. and Okubo A., Modeling Social Animal Aggregations[J]. in Frontiers in Theoretical Biology. New York: Springer-Verlag, Vol. 100,1994, pp. 296-325.
[16] Toner J. and Tu Y., Flochs, Herds, and Schools: a Quantitative Theory of Flocking[J]. Phys. Rev. E, Vol. 58, No.4,1998, pp.4828-4858.
[17] Bonabeau E., Dorigo M., and Theraulaz G., Swarm Intelligence: From Natural to Artificial Systems[M]. New York: Oxford Univ. Press, 1999.
[18] Giulietti F., Pollini L. and Innocenti M., Autonomous Formation Flight[J]. IEEE Control Syst. Mag., Vol. 20, No. 10, 2000, pp. 34-44.
[19] Burgard W., Moors M., Stachniss C. and Schneider F. E., Coordinated Multi-Robot Ex-ploration[J]. IEEE Transactions on Robotics, Vol.21, No.3,2005,pp.376-386.
[20] Ahmad R., Lee Yung-Chuan, Rahimi S., Gupta B., A Multi-Agent Based Approach for Particle Swarm Optimization[C]. Integration of Knowledge Intensive Multi-Agent Systems, 2007. KIMAS 2007. International Conference on April 30 2007, pp. 267-271.
[21] Mazurowski M.A. and Zurada J.M., Solving Multi-agent Control Problems Using Particle Swarm Optimization[C]. Swarm Intelligence Symposium, 2007. SIS 2007. IEEE 1-5 April 2007 pp. 105-111
[22] Balch T. and Arkin R. C., Behavior-Based Formation Control for Multirobot Teams[J]. IEEE Trans. Robot. Automat., Vol. 14, No. 12, 1998, pp. 926-939.
[23] Suzuki I. and Yamashita M., Distributed Anonymous Mobile Robots: Formation of Geometric Patterns[J]. SIAM J. Comput., Vol. 28, No. 4, 1999, pp. 1347-1363.
[24] Yamaguchi H., A Cooperative Hunting Behavior by Mobile-Robot Troops[J]. Int. J. Robot. Res., Vol.18, Sept. 1999, pp. 931-940.
[25] Maurizio Porfiri, Roberson D. Gray and Stilwell Daniel J., Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach[J]. Automatica Vol.43, 2007, pp. 1318-1328.
[26] Jongeun Choi, Joonho Lee, Songhwai Oh, Biologically-Inspired Navigation Strategies for Swarm Intelligence Using Spatial Gaussian Processes[C]. To be appeared in the 17th International Federation of Automatic Control(2008.7).
[27] Tanner H. G., Pappas G. J., Kumar V., Leader-to-Formation Stability[J]. IEEE Trans. Autom. Robot., Vol.20, No.3,2004, PP. 443-455.
[28] Lafferriere G, Williams A, Caughman J, Veerman JJP. Decentralized Control of Vehicle Formations[J]. Systems and Control Letters, Vol.54, No.9,2005, pp. 899-910.
[29] Lin Zhiyun, Bruce Francis and Manfredi Maggiore, Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles[J]. IEEE Trans. Automat. Control, Vol.50, No.l,2005,pp.l21-127.
[30] Bulentozguler A., Global Stabiliztion Via Local Stabilizing Actions[J]. IEEE Trans. Automat. Control,Vol.51, No.3,2006, PP.530-533.
[31] Reif J. H. and Wang H., Social Potential Fields: a Distributed Behavioral Control for Autonomous Robots[J]. Robot. Auton. Syst., Vol. 27, 1999, pp. 171-194.
[32] Desai J. P., Ostrowski J. and Kumar V, Controlling Formations of Multiple Mobile Robots[C]. in Proc. IEEE Int. Conf. Robot. Automat., Leuven, Belgium, May 1998, pp. 2864-2869.
[33] Egerstedt M. and Hu X., Formation Constrained Multi-Agent Control[J]. IEEE Trans Robot. Automat., Vol. 17, Dec. 2001, pp. 947-951.
[34] Reynolds C. W., Flocks, Birds, and Schools: A Distributed Behavioral Model[J]. Comput. Graph., Vol.21, 1987, pp. 25-34.
[35] Vicsek X, Czirok A., Ben-Jacob E., Cohen I. and Shochet O., Novel Type of Phase Transition in a System of Self-Driven Particles[J]. Phys. Rev. Lett., Vol. 75, No. 6, 1995, pp. 1226-1229.
[36] Czirok A., Ben-Jacob E., Cohen I., and Vicsek T., Formation of Complex Bacterial Colonies Via Self-Generated Vortices[J]. Phys. Rev. E., Vol. 54, No. 2, 1996, pp. 1791-1801.
[37] Czirok A., Stanley H. E., and Vicsek T., Spontaneously Ordered Motion of Self-propelled Particles[J]. J. Phys. A: Math Nucl. General, Vol. 30, 1997, pp. 1375-1385.
[38] Czirok A. and Vicsek T., Collective Behavior of Interacting Self-Propelled Particles[J]. Physica A, Vol. 281,2000, pp. 17-29.
[39] Shimoyama N., Sugawa K., Mizuguchi T., Hayakawa Y., and Sano M., Collective Motion in a System of Motile Elements[J]. Phys. Rev. Lett., Vol. 76, No. 20,1996, pp. 3870-3873.
[40] Levine H. and Rappel W.-J., Self-Organization in Systems of Self-Propelled Particles[J]. Phys. Rev. E, Vol. 63, No. 1, January 2001, pp. 017 101-1-017 101-4.
[41] Fax J. A. and Murray R. M., Information Flow and Cooperative Control of Vehicle For-mations[J]. IEEE Trans. Automat. Control, Vol.49, No.9,2004, pp. 1465-1476.
[42] Jadbabaie A., Lin J.and Morse S. A., Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules[J]. IEEE Trans. Automat. Control, Vol.48, No.6, 2003, pp. 988-1000.
[43] Moshtagh N. and Jadbabaie A., Distributed Geodesic Control Laws for Flocking of Non-holonomic Agents[J]. IEEE Trans. Automat. Control, Vol.52, No.4, 2007, pp. 681-686.
[44] S. Prajna, A. Jadbabaie, G. J. Pappas, A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates[J]. IEEE Trans. Automat. Control, Vol.52, No.8, 2007, pp. 1415-1428.
[45] Tanner H. G., Jadbabaie A. and Pappas G. J., Flocking in Fixed and Switching Net-works[J]. IEEE Trans. Automat. Control, Vol.52, No.5, 2007, pp. 863-868.
[46] Tsitsiklis J. N. and Bertsekas D. P.. Comment on Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules[J]. IEEE Trans. Automat. Control, Vol. 52, No. 5, 2007, pp. 968-969.
[47] Ren W. and Beard R. W., Consensus Seeking in Multiagent Systems Under Dynamically Changing Interaction Topologies[J]. IEEE Trans. Automat. Control,, Vol.50,2005, pp.655-661.
[48] Saber, R.O. and Murray, R.M., Consensus Problems in Networks of Agents with Switching Topology and Time-Delays[J]. IEEE Trans. Automat. Control, Vol.49, No.9,2004, pp. 1520-1533.
[49] Saber R.O., Fax J. A. and Murray R.M., Consensus and Cooperation in Networked Multiagent Systems[J]. Proceedings of the IEEE,, Vol.95, No.1, 2007, pp. 215-240.
[50] Fang L., Antsaklis P. J., and Tzimas A., Asynchronous Consensus Protocols: Preliminary Results, Simulations and Open Questions[C]. in 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC ' 05), Dec. 2005, pp. 2194-2199.
[51] Dimarogonas D. V. and Kyriakopoulos K. J., Formation Control and Collision Avoidance for Multi-Agent Systems and a Connection between Formation Infeasibility and Flocking Behavior[C]. in 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC ' 05), Dec. 2005, pp. 84-89.
[52] Lin Z., Brouke M., and Francis B., Local Control Strategies for Groups of Mobile Autonomous Agents[J]. IEEE Trans. Autom. Control, Vol.49, No.4, 2004, pp. 622-629.
[53] Moreau L., Stability of Multiagent Systems with Time-Dependent Communication[J]. IEEE Trans. Automat. Control, Vol.50, No.l, 2005, pp. 169-182.
[54] Olfati-Saber R., Ultrafast Consensus in Small-World Networks[C]. ACC, 2005, pp. 2371-2378.
[55] Cortes J., Achieving Coordination Tasks in Finite Time Via Nonsmooth Gradient-flows[C]. in Proc. 44th IEEE Conf. Decision and Control, 2005 and 2005 Eur. Control Conf. (CDC-ECC '05), Dec. 2005, pp. 6376-6381.
[56] Olfati-Saber R., Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory[J]. IEEE Trans. Autom. Control, Vol. 51, No. 3, 2006, pp. 401-420.
[57] Lin Z., Francis B., and Maggiore M., State Agreement for Continuous-Time Coupled Nonlinear Systems[J]. SIAM Journal on Control and Optimization, Vol.46, No.l, 2007, pp.288-307.
[58] Xiao L. and Boyd S., Fast Linear Iterations for Distributed Averaging[J]. Systems and Control Letters, Vol. 53, 2005, pp. 65-78.
[59] Angeli D. and Bliman P. A., Stability of Leaderless Discrete-Time Multi-Agent Sys-tems[J]. Mathematics of Control, Signals, and Systems, Vol.18, 2006, pp. 293-322.
[60] Hayashi N., Ushio T., Harada F. and Ohno A., Consensus Problem of Multi-Agent Systems with Nonlinear Performance Functions[C].IEICE Fundamentals, E90-A 2007(10), pp. 2261-2264.
[61] Bauso D., Giarre L., and Pesenti R., Nonlinear Protocols for Optimal Distributed Consensus in Networks of Dynamic Agents[J]. Systems and Control Letters, Vol. 55, No.11, 2006, pp.918-928.
[62] Albert B. and Barabasi A.-L., Statistical Mechanics of Complex Networks[J]. Reviews of Modern Physics, Vol.74, 2002, pp. 47-97.
[63] Hatano Y. and Mesbahi M., Agreement Over Random Networks[J]. IEEE Trans. Autom. Control, Vol. 50, No. 11,2005, pp. 1867-1872.
[64] Blondel V. D., Hendrickx J. M., Olshevsky A. and Tsitsiklis J. N.. Convergence in Mul-tiagent Coordination, Consensus, and Flocking[C]. Proceedings of the Joint 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain. 2005.
[65] Gazi V. and Passino K. M., Stability Analysis of Swarms[J]. IEEE Trans. Automat. Contr., Vol.48, No.4,2003, pp. 692-697.
[66] Gazi V. and Passion K.M., Stability Analysis of Social Foraging Swarms[J]. IEEE Trans. System, man and Cybernetics-B, Vol.34, No.1, 2004, pp.539-557.
[67] Gazi V. and Passino K.M., Stability of a One-Dimensional Discrete-Time Asynchronous Swarm[J]. Systems, Man and Cybernetics, Part B, IEEE Transactions on Volume 35, Issue 4,Aug.2005,pp.834-841.
[68] Gazi V, Swarm Aggregations Using Artificial Potentials and Sliding-mode Control[J]. Robotics, IEEE Transactions on [see also Robotics and Automation, IEEE Transactions on], Vol. 21, Issue 6, Dec. 2005, pp. 1208-1214.
[69]Gazi V.,Stability of an Asynchronous Swarm With Time-Dependent Communication Links[J].Systems,Man,and Cybernetics,Part B,IEEE Transactions on,Vol.38,Issue 1,Feb.2008,pp.267-274.
[70]Liu Y.and Passino K.M.,Stable Social Foraging Swarms in a Noisy Environment[J].IEEE Trans.Automat.Control,Vol.49,No.1,2004,pp.30-44.
[71]Liu Y.and Passino K.M.,Cohesive Behaviors of Multiagent Systems With Information Flow Constraints[J].Automatic Control,IEEE Transactions on,Vol.51,Issue 11,Nov.2006,pp.1734-1748.
[72]Savkin,A.V.,Coordinate Collective Motion of Groups of Autonomous Mobile Robots:Analysis of Vicsek's Model[J].IEEE Trans.Automat.Control,Vol.49,No.6,2004,pp.981-983.
[73]Liu Y.,Passino K.M.and Polycarpou M.M.,Stability Analysis of One-Dimensional Asynchronous Swarms[J].IEEE Transactions on Automatic Control,Vol.48,No.10,2003,pp.1848-1854.
[74]Savkin A.V.,Coordinated Collective Motion of Groups of Autonomous Mobile Robots:Analysis of Vicsek' s Model[J].IEEE Trans.Autom.Contr.,Vol.49,No.6,2004,pp.981-983.
[75]Liu Y.,Passino K.M.and Polycarpou M.,Stability Analysis of m-Dimensional Asynchronous Swarms with a Fixed Communication Topology[J].IEEE Trans.Automat.Contr.,Vol.48,No.1,2003,pp.76-95.
[76]程代展,陈翰馥.从群集到社会行为控制[J].科技导报,No.8,2005,pp.4-7.
[77]Guo L.,Liu Z.and Han J.,Multi-Agent Systems with Local Rules:Towards a Theory of Analysis and Control[C].Chinese Contr.Conf.,43,2006.
[78]楚天广,陈志绣,王龙,谢广明.群体动力学与协调控制[C].第二十六届中国控制会议论文集,2007.
[79]Chen Z.and Chu T.,Aggregation and Pattern Formation of Multi-Agent System[J].Chinese Contr.Conf.,2007,pp.26-31.
[80] Shi H., Wang L. and Chu T., Swarming Behavior of Multiagent Systems[J]. J. Contr. Theory Appl., Vol.2, No.4,2004, pp.313-318.
[81] B. Liu, T. Chu, L. Wang, Z. Wang, Swarm dynamics of a group of mobile autonomous agents[J]. Chinese Phys. Lett., Vol.22, 2005, pp. 254-257.
[82] Liu, Bo; Xie, Guangming; Chu, Tianguang; Wang, Long, Controllability of Interconnected Systems via Switching Networks with a Leader Systems[C]. Man and Cybernetics, 2006. ICSMC '06. IEEE International Conference on Volume 5, 8-11 Oct. 2006 pp.3912-3916.
[83] Leng Cuiping, Zheng Yufan and Yu Hongwang, A Formation Control for Dynamical Agents in Digital Network[C].The 6th International Conference on Control and Automation (IEEE ICCA), 2007.5.
[84] Chu T., Wang L., Chen T. and Mu S., Self-Organized Motion in a Class of Anisotropic Swarms: Convergence vs Oscillation[J]. Chaos, Solitons Fractals, Vol.30, 2006, pp.875-885.
[85] Mu S., Chu T. and Wang L., Coordinated Collective Motion in a Motile Particle Group With a Leader[J]. Physica A, Vol.351,2005, pp.211-226.
[86] Shi H., Wang L. and Chu T., Virtual Leader Approach to Coordinated Control of Multiple Mobile Agents with Asymmetric Interactions[J]. Physica D, Vol.213, 2006, pp.51-65.
[87] Hong Y., Gao L., Cheng D. and J. Hu, Lyapunov-Based Approach to Multiagent Systems with Switching Jointly Connected Interconnection[J]. IEEE Trans. Autom. Contr., Vol.52, No.5, 2007,pp.943-948.
[88] Jiangping Hu and Yiguang Hong, Leader-Following Coordination of Multi-Agent Systems with Coupling Time Delays[J]. Physica A, Vol.374, 2007, pp. 853-863.
[89] Xiao F., Wang L. and Wang A., Consensus Problems in Discrete-Time Multiagent Systems with Fixed Topology[J]. J. Math. Anal. Appl., Vol.322, No.2, 2006, 587-598.
[90] Sun Yuan Gong, Wang Long and Xie Guangming, Average Consensus in Directed Networks of Dynamic Agents with Time-Varying Communication Delays[C].Decision and Control, 2006 45th IEEE Conference on 13-15 Dec. 2006, pp.3393-3398.
[91] Sun Yuan Gong, Wang Long and Xie Guangming, Average Consensus in Networks of Dynamic Agents with Switching Topologies and Multiple Time-Varying Delays[J]. Systems and Control Letters, Vol.57,No.2, 2008, pp: 175-183.
[92] Bliman P. A. and Ferrari-Trecate G., Average Consensus Problems in Networks of Agents with Delayed Communications[C]. Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on 12-15, Dec. 2005,pp.7066-7071.
[93] Lee Dongjun and Spong Mark W., Agreement with Non-Uniform Information Delays[C]. Proceedings of the 2006 American Control Conference, 2006, pp. 756-761.
[94] Gu Dongbing, Distributed Particle Filter for Target Tracking[C]. Robotics and Automation, 2007 IEEE International Conference on 10-14, April 2007, pp.3856-3861.
[95] Jin Zhipu and Murray Richard M, Random Consensus Protocol in Large-Scale Net-works[C]. Decision and Control, 2007 46th IEEE Conference on 12-14, Dec. 2007, pp.4227-4232.
[96] Chen Jen-Yeu and Hu Jianghai, On the Convergence of Distributed Random Grouping for Average Consensus on Sensor Networks with Time-Varying Graphs[C]. Decision and Control, 2007 46th IEEE Conference on 12-14, Dec. 2007 pp.4233-4238.
[97] Xiao F. and Wang L., State Consensus for Multi-Agent Systems with Switching Topologies and Time-Varying Delays[J]. Int. J. Control, Vol.79, No. 10, 2006, pp. 1277-1284.
[98] Xiao F. and Wang L., Dynamic Behavior of Discrete-Time Multiagent Systems with General Communication Structures[J]. Physica A, Vol.370, No.2, 2006, pp.364-380.
[99] Xiao Feng, Wang Long and Jia Yingmin, Fast Information Sharing in Networks of Autonomous Agents. To be appeared in American Control Conference(2008).
[100] Liu Y., Jia Y., Du J. and Yu F., Average-Consensus Problems in Multiagent Sys-tems[C].European Control Conference, 2007.
[101] Chu T., Wang L. and Chen T., Self-Organized Motion in a Class of Anisotropic Swarms: Convergence vs Oscillation[C]. Proceedings of American Control Conference, 8-10 June 2005 ,vol. 5, 2005, pp.3474-3479.
[102] Lin Peng, Jia Yingmin, Average Consensus in Networks of Multi-Agents with Both Switching Topology and Coupling Time-Delay[J]. Physica A, Vol.387,2008, pp. 303-313.
[103] Xie Guangming and Wang Long, Consensus Control for a class of Networks of Dynamic Agents[J]. Int. J. of Robust and Nonlinear Control, Vol.17, 2007, pp.941-959.
[104] Hong Y., Hua J. and Gao L., Tracking Control for Multi-Agent Consensus with an Active Leader and Variable Topology[J]. Automatica, Vol.42, 2006, pp. 1177-1182.
[105] Maurizio Porfiri and Daniel J. Stilwell, Consensus Seeking Over Random Weighted Directed Graphs[J]. IEEE Trans. Autom. Control, Vol. 52, No. 9, Dec. 2007, pp. 1767-11773.
[106] Kar S., Moura J. M. F., Distributed Average Consensus in Sensor Networks with Random Link Failures[C]. Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on Volume 2, 15-20 April 2007, pp.II-1013-II-1016.
[107] Patterson Stacy , Bamieh Bassam and El Abbadi Amr, Distributed Average Consensus with Stochastic Communication Failures[C]. Decision and Control, 2007 46th IEEE Conference on 12-14 Dec. 2007, pp.4215-4220.
[108] Fagnani F. and Zampieri S., Randomized Consensus Algorithms Over Large Scale Net-works[C]. Information Theory and Applications Workshop, 2007 Jan. 29 2007-Feb. 2 2007, pp. 150-159.
[109] Tahbaz-Salehi A. and Jadbabaie A., On Consensus in Random Networks[C]. Allerton Conference on Communication, Control, and Computing, Allerton House IL, 2007.
[110] David Angeli and Pierre-Alexandre Bliman, Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees[J]. arXiv: math/0610854v1, 2007.
[111] Fiedler M., Algebraic Connectivity of Graphs[J]. Czechoslovak Math. J., Vol. 23, No. 98, 1973, pp. 298-305.
[112] Merris R., Laplacian Matrices of a Graph: A Survey[J]. Linear Algebra its Appl., Vol. 197, 1994, pp. 143-176.
[113] Biggs N., Algebraic, Graph Theory[M]. Cambridge University Press, Combridge, 1994.
[114]Hom R.A.and Johnson C.R.,Matrix Analysis[M].Cambridge,U.K.:Cambridge Univ.Press,1987.
[115]郑大钟,《线性系统理论》[M].北京:清华大学出版社,2002.
[116]黄琳,稳定性与鲁棒性的理论基础[M].北京:科学出版社,2003.
[117]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用[M].北京:清华大学出版社,2003
[118]Isidori A.,Nonlinear Control Systems Ⅱ[M].Communications and Control Engineering Series.Springer-Vedag,London,1999.
[119]Khalil H.K.,Nonlinear Systems(2nd ed.)[M].Upper Saddle River,N J:Prentice-Hall,1996.
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