复杂网络建模与一致性及在多移动智能体中的应用
|
摘要
自1998年的Watts和Strogatz提出“小世界”网络模型,1999年Barabàsi和Albert提出“无标度”网络演化模型以来,复杂网络的研究在实证分析、网络的演化模型、网络的动力学行为和复杂网络理论的应用这四个方面取得了惊人的进展。在机器人及人工智能领域,多移动智能体的协调控制是当前的一个热点问题。受到当前复杂动态网络理论迅速发展的启发,将多移动智能体系统看成一个复杂动态网络,网络中的节点表示智能体,两个节点之间的边表示两智能体之间的协作关系(比如感应关系、通信关系等),节点的动力学特性则表示智能体群运动特性。本文以多移动智能体系统为研究背景,以复杂网络理论为工具,在网络建模、网络的一致性问题等方面展开了研究,本文主要工作如下:
受多移动智能体通信网络的启发,提出了一类基于物理位置近邻的演化网络模型。在这些模型的基础上,对这些模型生成的网络的聚类系数、平均路径长度、度分布、对网络延时的鲁棒性和达到一致性所需要的时间等在不同的演化参数下不同的特性作了深入研究。研究表明,随着近邻节点数M的增大,这5个模型产生的网络的聚类系数都急剧减小、一致性问题收敛时间都会变短;对于模型4,它对网络延时的鲁棒性是最差,当M由小变大时,其度分布由指数分布到幂律分布过渡,BA无标度模型仅仅是它的一种特殊(极限)情况。
研究了几种不同拓扑结构的网络对节点失效和边失效的鲁棒性、对网络延时的鲁棒性以及一致性问题的收敛速度等方面的特性,这些网络包括小世界网络、无标度网络、最临近耦合网络、星网络和全耦合网络等。通过研究发现,第一,星网络作为一个边较少的网络,却具有很快的一致性问题收敛速度,其收敛速度要比和它具有相同节点数和节点平均度的小世界网络和无标度网络都要快,但星网络对网络延时的鲁棒性很弱;第二,小世界网络和无标度网络在相同平均度和节点数的情况下,其一致性问题的收敛速度相差不大,但它们要比和它们具有相同平均度和节点数的最邻近耦合网络的收敛速度快很多倍;第三,全耦合网络是所有网络中一致性收敛速度最快的,但其对网络延时的鲁棒性很弱;第四,网络节点最大度和网络的延时鲁棒性有近似的线性关系,因此网络节点的最大度可以用来对网络延时鲁棒性进行预测;最后,对无标度网络而言,通过对网络中很小一部分边进行解耦,可以显著提高网络对延时的鲁棒性。
提出了设计一致性速度优化的小世界网络的两种方法。一种基于NW小世界网络模型(由Newman和Watts提出)和遗传算法,另一种是基于WS小世界模型(由Watts和Staogtz提出)和长程节点优先连接。研究表明,当使用NW模型来构建节点数不多、长程连接数固定的小世界网络时,可以使用遗传算法来优化选择长程连接的连接图,以获得小世界网络更快的一致性收敛速度;当使用WS模型来构建小世界网络,在断边重连的每一步,当重连的另一个节点选择和固定节点距离最长的节点时,所形成的小世界网络的一致性收敛速度会明显加快。
受复杂动态网络一致性理论的启发,提出了一个简单新颖的、适用固定和动态变化两种通信拓扑的多移动智能体系统的队形控制和群运动控制模型。在该模型的基础上,使用复杂网络的一致性理论,给出和证明了两个关于系统在固定和动态变化通信拓扑下的系统稳定性的两个定理。
受复杂动态网络的同步理论的启发,提出了另一个多移动智能体系统的队形控制和群运动控制的控制器设计方案,并为系统给出了一个新颖的控制模型。在该模型的基础上,研究了每一个智能体的控制器的具体设计方案,对系统的稳定性进行了分析和证明。该方案更适用于智能体运动特性特别复杂的情况。
群集运动控制是模拟自然界中生物聚集运动的新型分布式控制方法,在当前多移动智能体群集控制理论的基础上,提出了基于领航者跟随者模式的动态变化拓扑的有序化群集运动控制算法,使得群集运动成为有序化控制行为。当智能体网络在切换的情况下,该方案设计出的控制输出仍然是光滑的。
最后对全文的研究工作进行了总结,并对将来要做的研究工作进行了展望。
Since Watts and Strigatz’s work in small-world network in 1998 and Barabàsi and Albert’s work in scale-free in 1999, an explosion of work about complex networks emerges, from the analysis of the topologies of real networks, the evolution models and dynamics of complex networks to the applications of the complex network theory. And in the field of Robotics and Artificial Intelligence, the coordinate control of multiple motion agent system (MMAS) is nowadays a hot topic. Motivated by the recent advances in theory of complex dynamical network, we regard MMAS as a complex dynamical network, where the node represents an agent, the edge between two nodes represents the coordinate relation (such as sensor relation or communication relation) between two agents and the dynamics of node represents the motion dynamics of agent. Based on complex dynamical network theory, the mode construction and consensus problem of multiple motion agent complex dynamical network are studied in this dissertation, and the main work and research results lie in the following.
Motivated by the communication network of MMAS, a class of evolving network models with physical position neighbourhood connectivity are proposed. Based on these models, the clustering coefficients, average distances, degree distributions, the tolerance to the network delay and the time to reach consensus for different evolving parameters in different models are studied detailedly. This study shows with the increasing of depth of neighbourhood M, the clustering coefficients decrease notably, the time to reach consensus becomes shorted in these five models. It also shows that Model 4 is most vulnerable to time-delay in these five models and its degree distribution represents a transition between that of an exponential network and that of a power-law scaling network with M increase, and the Barábasi-Albert scale-free model is only one of its special (limiting) cases.
We study the robustness to node and edge failure, the tolerance to network time-delay and the time to reach a consensus for different complex network topologies. And the topologies include small-world network, scale-free network, nearest neighbour coupled network, star network and global coupled network. By this study, we find the following results: First, as a topology with fewer edges, star network has a rapid convergence speed in the consensus problem, and its speed is faster than that of small-world network and scale-free network, which have the same number of node and average node degree. However, star network is vulnerable to time-delay. Second, the small-world network and scale-free network have the similar convergence speeds in consensus problem, and their convergence speeds are many times larger than that of the nearest neighbour coupled network with the same number of node and average node degree. Third, for global network, its speed is the fastest among all networks, but it is vulnerable to time-delay. Fourth, there is a near linear relationship between the robustness to time-delay and the maximum node degree of the network, so the maximum node degree of the network is a good predictor for time-delay robustness in all networks. Finally, for scale-free network, the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges of the network.
Two methods of devising a speed-optimized small-world network in consensus problem are presented. One bases on NW model (proposed by Newman and Watts) and genetic-algorithm (GA), another bases on WS model (proposed by Watts and Staogtz) and long-range nodes preference reconnection. It is found that, as we construct a small-world network with a smaller network size and fixed long-range links using NW model, we can optimize the long-range link configuration using GA methodology to obtain a small-world network with faster consensus speed. It is also find that in the every step of edges rewiring of small-world construction using WS model, as the distance between two rewiring nodes are the longest, the resulting network is faster significantly in reaching consensus.
Motivated by recent advances in consensus theory of complex dynamical network, we present a novel motion model about the formation control and group motion control of MMAS for fixed and changing interactions. Based on this model and the consensus theory of complex network, two theorems about motion stability of MMAS with fixed and switched topology are presented and proved.
Motivated by recent advances in synchronization theory of complex dynamical network, we develop another method of controller design for formation reaching and group motion controlling of the MMAS. A novel motion model of the system is presented. Based on this model, the design method of decentralized controller for each agent is investigated. The stability property of the system is also analyzed and proved in detail. This control method is useful espically as the motion dynamics of agent is complicated.
Flocking control is a new pattern of decentralized approach imitating animal cooperative behavior. A leader-follower flocking control mechanism for changing topology is introduced based on existed theory on flocking of mobile agents, which makes flocking motion be sequencable behaviour. The control output of this scheme is smooth even as the agent network is switching.
Finally, a summary has been done for all the discussion in the disseration. And the research work in further study is presented.
受多移动智能体通信网络的启发,提出了一类基于物理位置近邻的演化网络模型。在这些模型的基础上,对这些模型生成的网络的聚类系数、平均路径长度、度分布、对网络延时的鲁棒性和达到一致性所需要的时间等在不同的演化参数下不同的特性作了深入研究。研究表明,随着近邻节点数M的增大,这5个模型产生的网络的聚类系数都急剧减小、一致性问题收敛时间都会变短;对于模型4,它对网络延时的鲁棒性是最差,当M由小变大时,其度分布由指数分布到幂律分布过渡,BA无标度模型仅仅是它的一种特殊(极限)情况。
研究了几种不同拓扑结构的网络对节点失效和边失效的鲁棒性、对网络延时的鲁棒性以及一致性问题的收敛速度等方面的特性,这些网络包括小世界网络、无标度网络、最临近耦合网络、星网络和全耦合网络等。通过研究发现,第一,星网络作为一个边较少的网络,却具有很快的一致性问题收敛速度,其收敛速度要比和它具有相同节点数和节点平均度的小世界网络和无标度网络都要快,但星网络对网络延时的鲁棒性很弱;第二,小世界网络和无标度网络在相同平均度和节点数的情况下,其一致性问题的收敛速度相差不大,但它们要比和它们具有相同平均度和节点数的最邻近耦合网络的收敛速度快很多倍;第三,全耦合网络是所有网络中一致性收敛速度最快的,但其对网络延时的鲁棒性很弱;第四,网络节点最大度和网络的延时鲁棒性有近似的线性关系,因此网络节点的最大度可以用来对网络延时鲁棒性进行预测;最后,对无标度网络而言,通过对网络中很小一部分边进行解耦,可以显著提高网络对延时的鲁棒性。
提出了设计一致性速度优化的小世界网络的两种方法。一种基于NW小世界网络模型(由Newman和Watts提出)和遗传算法,另一种是基于WS小世界模型(由Watts和Staogtz提出)和长程节点优先连接。研究表明,当使用NW模型来构建节点数不多、长程连接数固定的小世界网络时,可以使用遗传算法来优化选择长程连接的连接图,以获得小世界网络更快的一致性收敛速度;当使用WS模型来构建小世界网络,在断边重连的每一步,当重连的另一个节点选择和固定节点距离最长的节点时,所形成的小世界网络的一致性收敛速度会明显加快。
受复杂动态网络一致性理论的启发,提出了一个简单新颖的、适用固定和动态变化两种通信拓扑的多移动智能体系统的队形控制和群运动控制模型。在该模型的基础上,使用复杂网络的一致性理论,给出和证明了两个关于系统在固定和动态变化通信拓扑下的系统稳定性的两个定理。
受复杂动态网络的同步理论的启发,提出了另一个多移动智能体系统的队形控制和群运动控制的控制器设计方案,并为系统给出了一个新颖的控制模型。在该模型的基础上,研究了每一个智能体的控制器的具体设计方案,对系统的稳定性进行了分析和证明。该方案更适用于智能体运动特性特别复杂的情况。
群集运动控制是模拟自然界中生物聚集运动的新型分布式控制方法,在当前多移动智能体群集控制理论的基础上,提出了基于领航者跟随者模式的动态变化拓扑的有序化群集运动控制算法,使得群集运动成为有序化控制行为。当智能体网络在切换的情况下,该方案设计出的控制输出仍然是光滑的。
最后对全文的研究工作进行了总结,并对将来要做的研究工作进行了展望。
Since Watts and Strigatz’s work in small-world network in 1998 and Barabàsi and Albert’s work in scale-free in 1999, an explosion of work about complex networks emerges, from the analysis of the topologies of real networks, the evolution models and dynamics of complex networks to the applications of the complex network theory. And in the field of Robotics and Artificial Intelligence, the coordinate control of multiple motion agent system (MMAS) is nowadays a hot topic. Motivated by the recent advances in theory of complex dynamical network, we regard MMAS as a complex dynamical network, where the node represents an agent, the edge between two nodes represents the coordinate relation (such as sensor relation or communication relation) between two agents and the dynamics of node represents the motion dynamics of agent. Based on complex dynamical network theory, the mode construction and consensus problem of multiple motion agent complex dynamical network are studied in this dissertation, and the main work and research results lie in the following.
Motivated by the communication network of MMAS, a class of evolving network models with physical position neighbourhood connectivity are proposed. Based on these models, the clustering coefficients, average distances, degree distributions, the tolerance to the network delay and the time to reach consensus for different evolving parameters in different models are studied detailedly. This study shows with the increasing of depth of neighbourhood M, the clustering coefficients decrease notably, the time to reach consensus becomes shorted in these five models. It also shows that Model 4 is most vulnerable to time-delay in these five models and its degree distribution represents a transition between that of an exponential network and that of a power-law scaling network with M increase, and the Barábasi-Albert scale-free model is only one of its special (limiting) cases.
We study the robustness to node and edge failure, the tolerance to network time-delay and the time to reach a consensus for different complex network topologies. And the topologies include small-world network, scale-free network, nearest neighbour coupled network, star network and global coupled network. By this study, we find the following results: First, as a topology with fewer edges, star network has a rapid convergence speed in the consensus problem, and its speed is faster than that of small-world network and scale-free network, which have the same number of node and average node degree. However, star network is vulnerable to time-delay. Second, the small-world network and scale-free network have the similar convergence speeds in consensus problem, and their convergence speeds are many times larger than that of the nearest neighbour coupled network with the same number of node and average node degree. Third, for global network, its speed is the fastest among all networks, but it is vulnerable to time-delay. Fourth, there is a near linear relationship between the robustness to time-delay and the maximum node degree of the network, so the maximum node degree of the network is a good predictor for time-delay robustness in all networks. Finally, for scale-free network, the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges of the network.
Two methods of devising a speed-optimized small-world network in consensus problem are presented. One bases on NW model (proposed by Newman and Watts) and genetic-algorithm (GA), another bases on WS model (proposed by Watts and Staogtz) and long-range nodes preference reconnection. It is found that, as we construct a small-world network with a smaller network size and fixed long-range links using NW model, we can optimize the long-range link configuration using GA methodology to obtain a small-world network with faster consensus speed. It is also find that in the every step of edges rewiring of small-world construction using WS model, as the distance between two rewiring nodes are the longest, the resulting network is faster significantly in reaching consensus.
Motivated by recent advances in consensus theory of complex dynamical network, we present a novel motion model about the formation control and group motion control of MMAS for fixed and changing interactions. Based on this model and the consensus theory of complex network, two theorems about motion stability of MMAS with fixed and switched topology are presented and proved.
Motivated by recent advances in synchronization theory of complex dynamical network, we develop another method of controller design for formation reaching and group motion controlling of the MMAS. A novel motion model of the system is presented. Based on this model, the design method of decentralized controller for each agent is investigated. The stability property of the system is also analyzed and proved in detail. This control method is useful espically as the motion dynamics of agent is complicated.
Flocking control is a new pattern of decentralized approach imitating animal cooperative behavior. A leader-follower flocking control mechanism for changing topology is introduced based on existed theory on flocking of mobile agents, which makes flocking motion be sequencable behaviour. The control output of this scheme is smooth even as the agent network is switching.
Finally, a summary has been done for all the discussion in the disseration. And the research work in further study is presented.
引文
[1] Strogatz S. H.. Exploring complex networks. Nature, 2001, 410:268-276.
[2] Wang X. F., Chen G.. Complex networks: small-world, scale-free and beyond. IEEE Circuits and Systems Magazine, 2003, First Quarter: 6-20.
[3]王树禾.图论.北京.科学出版社.2004.
[4]汪小帆,李翔,陈关荣.复杂网络及应用.北京.清华大学出版社. 2006.
[5] Erdos P., Renyi A.. On random graphs. Publications Mathematicae. 1959, 6: 290-297.
[6] Erdos P., Renyi A.. On the evolution of random graphs. Publications Mathematicae. Inst. Hung. Acad. Sci. 1960.
[7] Erdos P., Renyi A.. On the strength of connectedness of a random graph. Acta Math. Sci. Hungary, 1961, 12: 261-267.
[8] Milgram S.. The small world problem. Psychology Today, 1967, 2:60-67.
[9] Watts D. J., Strogatz S. H.. Collective dynamics of“small-world”networks. Nature, 1998, 393:440- 442.
[10] Barabàsi A .-L., Albet R.. Emergence of scaling in random networks. Science, 1999, 286:509-512.
[11] Albert R, Barabàsi A-L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74(1): 47-97.
[12] Barrat A, Weigt M.. On the properties of small world networks. Eur. Phys. J. B, 2000, 11:547-560.
[13] Newman M. E. J., Watts D. J.. Renormalization group analysis of the small-world network model. Phys. Lett. A, 1999, 263:341-346.
[14] Newman M. E. J., Watts D. J. Scaling and percolation in the small-world network model. Phys Rev. E, 1999, 60: 7332-7342.
[15] Newman M. E. J.. Models of the small-world. Journal of Statistical Physics, 2000, 101: 819-841.
[16] Goh K.-I., Kahng B., Kim D. .Universal Behavior of Load Distribution in Scale-Free Networks.Phys. Rev. Lett., 2001, 87: 278701-27874.
[17] Fan J, Wang X F. A wavelet of small-world networks. IEEE Trans. Circuits and Systems II, 2005,52(5):238-242.
[18] Barthelemy M., Amaral L. A. N.. Small-world networks: Evidence for acrossover picture. Phys Rev. Let., 1999, 82: 3180-3183.
[19] Cancho R. F., Janssen C., Sole R. V.. Topology of technology graphs: Small world paterns in electronic circuits. Phys. Rev. E, 2001, 64: 046119-046123.
[20] Ozana M.. Incipient spanning cluster on small-world networks. Europhys. Let., 2001, 55:762-766.
[21] Comellasa F., Sampels M.. Deterministic small-world networks. Physica A, 2002, 309: 231-235.
[22] Comellasa F., Ozbna J., Petersb J. G.. Deterministic small-world communication networks. Information Processing Leters, 2000, 76: 83-90.
[23] Monasson R.. Diffusion, localization and dispersion relations on‘small-world’lattices. Eur. Phys. J. B, 1999, 12:555-567.
[24] Arcangelis L. D., Herrmann H. J.. Self-organized criticality on small world networks. Physica A, 2002, 308: 545-549.
[25] Cosenza M. G, Tucci K.. Turbulence in small-world networks. Phys. Rev. E, 2002, 63:036223-036229.
[26] Hou Z., Xin H.. Oscillator death on small-world networks. Phys. Rev. E, 2003, 68:055103-055106.
[27] Gao Z., Hu B., Hu G.. Stochastic resonance of small-world networks. Phys. Rev. E, 2001, 65:016209-016212.
[28] Price D J . Networks of scientific papers. Science, 1965, 149(3683): 510-515.
[29] Bollobas B, Riordan O.. Mathematical results on scale-free random graphs. In Bornholdt, S, Schuster H G (ed.) Handbook of Graphs and Networks: From the Genome to the Internet, Berlin: Wiley-VCH, 2003, 1-34.
[30] Cohen R, Havlin S.. Scale-free networks are ultrasmall. Phys. Rev. Lett., 2003, 90: 058701-058704.
[31] Fronczak A, Fronczak P, Hilyst J A.. Mean-field theory for clustering coefficients in Barabàsi-Albert networks. Phys. Rev. E, 2003, 68:046126- 046129.
[32] Barabàsi A. -L., Albert R., Jeong H.. Scale-free characteristics of random networks: The topology of the World Wide Web. Physica A, 2000, 281: 9-77.
[33] Valverde S., Cancho R.F., Sole R. V.. Scale-free networks from optimal design. Eumphys Lett., 2002, 60:512-517.
[34] Caldarelli G., Capocci A., De Los Rios P. et al. Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett., 2002, 89: 258702-258705.
[35] Pastor-Satorras R., Vespignani A.. Epidemic spreading in scale-free networks. Phys. Rev. Lett., 2001, 86: 3200-3203.
[36] Pastor-Satorras R., Vespignani A.. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E, 2002, 65: 035108-035111.
[37] May R. M., Lloyd A. L.. Infection dynamics on scale-free networks. Phys. Rev. E, 2001, 64: 066112-066115.
[38] Lynch N. A.. Distributed Algorithms. Morgan Kaufmann Publishers, Inc,1997.
[39] DeGroot M. H.. Reaching a consensus. Journal of American Statistical Association, 1974, 69(345): 118-121.
[40] Benediktsson J. A., Swain P. H.. Consensus theoretic classification methods. IEEE Trans. on Systems, Man and Cybernetics, 1992, 22(4): 688-704.
[41] Saber R. O., Murray R. M.. Consensus protocols for networks of dynamic agents. Proc. 2003 ACC, 2003, 2: 951–956.
[42] Saber R. O., Murray R. M.. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Contr., 2004, 49( 9): 1520-1533.
[43] Saber R. O.. Ultrafast consensus in small-world network. Proc. ACC, Portland, OR, 2005, 4:2371-2378.
[44] Ren W., Beard R. W.. Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. on Automatic Control, 2005, 50(5): 655-660.
[45] Moreau L.. Stability of continuous-time distributed consensus algorithms. Proc. Of CDC, 2004, 4:3998-4003.
[46] Wang X. F., Chen G.. Synchronization in small-world dynamical networks. Int. J. Bifurcation and Chaos, 2002, 12 (1):187-192.
[47] Wang X. F., Chen G.. Synchronization in scale-free dynamical networks- robustness and fragility. IEEE Trans. CAS-I, 2002, 49: 54-62.
[48] Wang X. F.. Complex networks: Topology, dynamics and synchronization. Int. J. Bifurcation and Chaos, 2002, 12: 885-916.
[49] Wang X. F., Chen G.. Synchronization in complex dynamical networks. J. Systems Science and Complexity, 2003, 16:1-14.
[50] Li X., Wang X. F., Chen G.. Synchronization in complex dynamical networks and its applications. Conf. on Growing Networks and Graphics in Statistical Physics, Finance, Biology and Social Systems, Rome, Italy, 2003.
[51] Li X., Chen G.. Synchronization and desynchronization of complex dynamical networks-An engineering viewpoint. IEEE Trans. CAS-I, 2003, 50: 1381-1390.
[52] Fan J., Wang X. F., On Synchronization in scale-free dynamical networks. Physica A, 2005, 349:443-451.
[53] Lu J., Yu X., Chen G.. Chaos synchronization of general complex dynamical networks. Physica A, 2004, 334: 281-302.
[54] Pecora L. M., Carroll T. L.. Synchronization in chaotic systems. Phys. Rev. Let., 1990, 64: 821-825.
[55] Rosenblum M. G., Pikovsky A. S., Kurths J.. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett., 1997, 78: 4193-4196.
[56] Mainieri R., Rehacek J.. Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett., 1999, 82: 3042-3045.
[57] Voss H. U.. Anticipating chaotic synchronization. Phys. Rev. E, 2000, 61:5115-5119.
[58] Li C., Xu H., Liao X. et al.. Synchronization in small-world oscillator networks with coupling delays. Physica A, 2004, 335(3-4): 359-364.
[59] Gelover-Santiago A. L., Lima R., Matinez-Mekler G.. Synchronization and cluster periodic solutions in globally coupled maps. Physca A, 2000, 283: 131-135.
[60] Li C., Xu H., Liao X. et al.. Synchronization in coupled map lattices with small-world delayed interactions. Physica A, 2004, 335(3- 4): 365-370.
[61] Pikovsky A.S., Rosenblum M.G., Osipov G.V. et al. Phase synchronization of chaotic oscillators by external driving. Physica D, 1997, 104: 219-238.
[62] Blasius B., Huppert A., Stone L.. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature (London), 1999, 399: 354-359.
[63] Allaria E., Arechi F. T., Digarbo A. etal. Synchronization of homoclinic chaos. Phy. Rev. Lett., 2001, 86: 791-794.
[64] Taherion S., Lai Y.-C.. Experimental observation of lag synchronization in coupled chaotic systems. Int. J. Bifur. Chaos, 2000, 10: 2587-2594.
[65] Osipov G. V., A. Pikovsky S., Rosenblum M. G. et al. Phase synchronization effects in a lattice of nonidentical Rossler oscillators. Phys. Rev. E, 1997, 55: 2353-2361.
[66] Zheng Z., Hu G., Hu B.. Enhancement of phase synchronization throughasymmetric couplings. Phys. Rev. E, 2000, 62: 7501-7504.
[67] Ren Wei, Beard R. W., Atkins E. M.. A Survey of Consensus Problems in Multi-agent Coordination. 2005 ACC, Portland, OR, USA, 3:1859-1864, 2005.
[68]杨文,汪小帆,李翔,一致性问题综述,Proc. of the 25th CCC, 2006,中国哈尔滨,1491-1495.
[69] Moreau L.. Stability of multi-agent systems with time-dependent communication links. IEEE Trans. On Automatic Control, 2005, 50:169-182.
[70] Fang Lei, Antsaklis P.J., Information consensus of asynchronous discrete-time multi-agent systems.ACC, 2005, 3:1883-1888.
[71] Ren W., Beard R. W., McLain T. W.. Coordination variables and consensus building in multiple vehicle systems. in Cooperative Control (V. Kumar, N. E. Leonard, and A. S. Morse, eds.). Springer-Verlag Series: Lecture Notes in Control and Information Sciences, 2004, 309: 171–188.
[72] Lin Z., Francis B., Maggiore M.. Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. on Automatic Control, 2005, 50(1):121–127.
[73] Fax J. A., Murray R. M.. Information flow and cooperative control of vehicle formations. IEEE Trans. on Automatic Control, 2004, 49: 1465–1476.
[74] Gupta V., Hassibi B., Murray R.. Stability analysis of stochastically varying formations of dynamic agents. in Proc. of CDC, (Maui, Hawaii), 2003, 504–509.
[75] Lawton J. R., Beard R. W., Young B.. A decentralized approach to formation maneuvers. IEEE Transactions on Robotics and Automation, 2003, 19: 933–941.
[76] Glavaski S., Chaves M., Day R. et al. Vehicle networks: Achieving regular formation. in Proc. of ACC, (Denver, CO), 2003, 4095–4100.
[77] Vicsek T., Czirok A., Jacob E. B. et al. Novel type of phase transitions in asystem of self-driven particles. Phys. Rev. Lett., 1995, 75:1226-1229.
[78] Lawton J. R., Beard R. W., Synchronized multiple spacecraft rotations. Automatica, 2002, 38(8)1359–1364.
[79] Ren W., Beard R. W.. Decentralized scheme for spacecraft formation flying via the virtual structure approach. AIAA Journal of Guidance, Control, and Dynamics, 2004, 27:73–82.
[80] Bauso D., Giarr L., Pesenti R.. Attitude alignment of a team of UAVs under decentralized information structure. in IEEE Internation Conference on Control Applications, (Istanbul, Turkey), 2003, 1:486-491.
[81] Lin J., Morse A. S., B. Anderson D. O.. The multi-agent rendezvous problem. in Proc. of CDC, (Maui, Hawaii), 2003, 1508–1513.
[82] Kingston D. B., Ren W., Beard R. W.. Consensus algorithms are input-to-state stable. in Proc. of ACC, 2005, 3:1686-1960.
[83] Kauffman S. A.. Metabolic stability and epigenesis in randomly constructed genetic nets. J. of Theoretical Biology, 1969, 22(3):437–467.
[84] Newman M. E. J.. Scientific collaboration networks. I. network construction and fundamental results. Physical Review E, 2002, 64(1):0161311–0161318.
[85] Kopell N., Ermentrout G. B.. Symmetry and phaselocking in chains of weakly coupled oscillators. Communications in Pure and Appl. Math., 1986, 39:623– 660.
[86] Kuramoto Y.. Chemical oscillators, waves, and turbulance. Springer, Berlin, 1984.
[87] Mirollo R. E., Strogatz S. H.. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math., 1990, 50:1645–1662.
[88] Strogatz S. H.. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D, 2000, 143:1– 20.
[89] Winfree A. T.. Biological rythms and the behavior of populations of coupled oscillators. J. Theoretical Biology, 1967, 16:15–42.
[90] Cortes J., Martinez S., Karatas T. et al.. Coverage control for mobile sensing networks. The IEEE Trans. on Robotics and Automation, 2004, 20(2):243–255.
[91] Estrin D., Govindan R., Heidemann J. et al.. Next century challenges: scalable coordination in sensor networks. Proc. of Mobile Computing and Networking, 1999, 263–270.
[92] Mogilner A., Edelstein-Keshet L.. A non-local model for a swarm. J. Math. Biology, 1999, 38:534–570.
[93] Topaz C. M., Bertozzi A. L.. Swarming patterns in a two dimensional kinematic model for biological groups. Journal on Applied Mathematics, 2004, 65(1):152 -174.
[94] Beard R. W., Lawton J., Hadaegh F. Y.. A feedback architecture for formation control. IEEE Transactions on Control Systems Technology, 2001, 9:777-790.
[95] Kang W., Yeh H.-H.. Coordinated attitude control of multi-satellite systems. International Journal of Robust and Nonlinear Control, 2002, 12:185-205.
[96] Proud A. W., Pachter M., D’Azzo J. J.. Close formation flight control. in Proceedings of the AIAA Guidance, Navigation, arid Corntrol Conference and Exhibit, (Portland,OR), American Institute of Aeronautics and Astronautics, 1999. AIAA-99-4207:1231-1246.
[97] Stilwell D. J., Bishop B. E.. Platoons of underwater vehicles. IEEE Control Systems Magazine, 2000, 20:45-52.
[98] Horn R. A., Johnson C. R.. Matrix Analysis. Cambridge University Press 1987.
[99] Fiedler M.. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 1973, 23(98):298–305.
[100] Barabàsi A.-L., Albert R., Jeong H.. Mean-field theory for scale-free random networks. Physica A, 1999, 272: 173-187.
[101] Li X, Chen G. R.. A local-world evolving network model. Physica A, 2003, 328(1-2):274-286.
[102] Estrada E., Rodriguez-Velazquez J A..Subgraph centrality in complex networks. Phys. Rev. E. 2005, 71:056103-056111.
[103] Estrada E, Rodriguez-Velazquez J. A.. Spectral measure of bipartivity in complex networks. Phys. Rev. E, 2005, 72: 046105-046110.
[104] De Aguiar M. A. M., Bar-Yam Y.. Spectral analysis and the dynamic response of complex nctwodcs. Phys Rev E, 2005, 71: 016106-016110.
[105] Farkas I., Dcrenyi I., Jeong H. et al.. Networks in life scaling properties and eigenvalue spectra. Physica A, 2002, 314: 25-34.
[106] Holland J H., Adaptation in natural and artificial systems. AnnArbor, Michigan: University of Michigan Press,1975.
[107] Goldberg D E.. Genetic algorithm in search, optimization and machine learning. Reading MA: Addison-Wesley Publishing Company,1989.
[108]张晓缋,方浩,戴冠中.遗传算法的编码机制研究.信息与控制, 1997, 26(2): 134~139.
[109] Takashi Nishikawa, Adilson E. M., Lai Ying-Cheng et al. Smallest small-world network. Phys. Rev. E, 2002, 66:046139-046143.
[110] Dias M. B., Stentz A.. A Market Approach to Multirobot Coordination. Technical Report CMU-R I-TR-01-26. Robotics Institute, Carnegie Mellon University, 2001.
[111] Balch T., Arkin R. C.. Behavior-based Formation Control for Multirobot Teams. IEEE Trans on Robotics and Aut., 1998, 14 (6) : 1-15.
[112] Parker L. E.. Adaptive Heterogeneous Multi-robot Teams. Neurocomputing, 1999, 28: 75-92.
[113]曹志强,张斌,谭民.基于行为的多移动机器人实时队形保持.高技术通信,2001,10:74-77.
[114] Desai J. P., Ostrowski J. P., Kumar V.. Controlling formations of multiple mobile robots. in Proceedings of IEEE int. Conference on Robotics and Automation, Leuven, Belgium, 1998, 2864-2869.
[115] Fierro R., Das A. K., Kumar V. et al. Hybrid Control of formations of Robots. in Proceedings of IEEE int. Conference Robotics and Automation, Seoul, Korea, 2001, 157-162.
[116] Desai J. P., Ostrowski J. P., Kumar V.. Modeling and Control of Formation of Nonholonomic Mobile Robots. IEEE int. transaction on Robotics and Automation. 2001, 17(6):905-908.
[117] Tanner H. G., Pappas G. J., Kumar V.. Leader to formation stability. IEEE Trans on Robotics and Automation, 2004, 20(3):443-455.
[118] Tan K.-H., Lewis M.. Virtual structures for high-precision cooperative mobile robotic control. in proceedings of the 1996 IEE/RSJ International conference, 1996,1:132-139.
[119] Leonard N. E., Fiorelli E.. Virtual Leader, Artificial Potentials and Coordinated Control of Groups. in proceedings of the 40th IEEE conference on Decision and Control , Orlando, Florida USA, 2001, 3:2968-2973.
[120] Ren W., Beard R. W.. Formation feedback control for multiple spacecraft via virtual structures, IEE Proc Control Theory and Applications, 2004, 3:357-368.
[121] Anthony L. M., Tan K. H.. High. precision formation control of mobile robots using virtual structures autonomous. Autonomuous Robots, 1974, 387-403.
[122] Brett J Y., Beard R. W., Kelsey J. M.. A control scheme for improving multi-vehicle formaion maneuvers, American Control Conf., Arlington, 2001, 704-709.
[123] Reynolds C. W.. Flocks, herds, and schools: A distributed behavioral model. Computer Graphics, 1987, 21(4): 25-34.
[124] Jadbabaie A, Lin J, Morse A. S.. Coordination of groups of mobile autonomousagents using nearest neighbor rules. IEEE Trans on Automatic Control, 2003, 48(6): 988-1001.
[125] Balch T, Hybinette M. Social potentials for scalable multi-robot formations. Proc. IEEE Int Conf. on Robotics and Automation. San Fransisco, 2000, 1: 73-80.
[126] Kostelnik P, Samulka M, Janosik M. Scalable multi-robot formations using local sensing and communication. Proc. of the 3rd Int Workshop on Robot Motion and Control. Poznan, 2002, 319-324.
[127] Lawton J., Young B., Beard R.. A decentralized approach to elementary formation maneuvers. IEEE Int Conf on Robotics and Automation. San Fransico, 2000, 3: 2728-2733.
[128]董胜龙,陈卫东,席裕庚.多移动机器人编队的分布式控制系统.机器人, 2000, 22(6): 433-438.
[129] Desai J P. A graph theoretic approach for modeling mobile robot team formations . J of Robotic Systems, 2002, 511-525.
[130] Saber R. O., Murray R. M.. Flocking with obstacle avoidance: cooperation with limited communication in mobile networks. Proc. Of the IEEE Conf. on Decision and Control, 2003, 2022-2028.
[131] Huygenii G.. Horoloquim oscilatoriumm. France: Parisiism, 1673.
[132] Winfree A. T.. Geometry of biological time. New York: Springer-Verlag, 1990.
[133] Buck J B, Buck E. Mechanism of rhythmic synchronous flashing of fireflies. Science, 1968, 159: 1319-1327.
[134] Buck J B. Synchronous rhythmic flashing of fireflies. Quarterly Review of Biology, 1938, 13: 301-314.
[135] Buck J B. Synchronous rhythmic flashing of fireflies II. Quarterly Review of Biology, 1988, 63: 265-289.
[136] Kaneko K.. Coupled Map Lattices. Singapore: World Scientific, 1992.
[137] Chua L O.. CNN: A paradigm for Complexity, Singapore: World Scientific, 1993.
[138] Gade P M.. Synchronization of oscillators with random nonlocal connectivity. Phys. Rev. E, 1996, 54 (1) :64-70.
[139] Gade P M, Hu C-K.. Synchronization and coherence in thermodynamic coupled map lattices with intermediate-range coupling. Phys. Rev. E, 1999, 60 (4):4966-4969.
[140] Gade P M, Hu C-K.. Synchronous chaos in coupled map lattices with small-world interactions. Phys. Rev. E, 2000, 62 (5):6409-6413.
[141]赵明,汪秉宏,蒋品群,周涛.复杂网络上动力系统同步的研究进展.物理学进展,2005,25(3):273-295.
[142]赵明,周涛,陈关荣,汪秉宏.复杂网络上动力系统同步的研究进展Ⅱ——如何提高网络的同步能力.物理学进展,2006,25(3):273-295.
[143] Kang W., Xi N., Spaks A.. Theory and Applications of Formation Control in a Perceptive Referenced Frame. in Proceedings of IEEE int. Conference on Decision and Control, Sydney, Australia, 2000, 352-357.
[144] Hiroaki Yamaguchi, Tamio Arai, Gerardo Beni. A distributed control scheme for multiple robotic vehicles to make group formations. ELSEVIER, Robotics and Automations System , 2001, 36:125-147.
[145]廖晓昕,稳定性的理论、方法和应用,华中理工大学出版社,1998.
[146] Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents, part I: fixed topology. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway: IEEE, 2003. 2010-2015.
[147] Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents, part II: dynamic topology. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway: IEEE, 2003,2016-2021.
[148] Tanner H G. Flocking with obstacle avoidance in switching networks ofinterconnected vehicles. Proceedings of the 2004 IEEE International Conference on Robotics and Automation. Piscataway: IEEE, 2004. 3006-3011.
[149]俞辉,王永骥.稳定的有领航者的多移动智能体群集运动控制.华中科技大学学报(自然科学版),2005,33(8):56-58.
[150] Saber R O. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Automat. Contr., 2006, 51(3):401-420.
[2] Wang X. F., Chen G.. Complex networks: small-world, scale-free and beyond. IEEE Circuits and Systems Magazine, 2003, First Quarter: 6-20.
[3]王树禾.图论.北京.科学出版社.2004.
[4]汪小帆,李翔,陈关荣.复杂网络及应用.北京.清华大学出版社. 2006.
[5] Erdos P., Renyi A.. On random graphs. Publications Mathematicae. 1959, 6: 290-297.
[6] Erdos P., Renyi A.. On the evolution of random graphs. Publications Mathematicae. Inst. Hung. Acad. Sci. 1960.
[7] Erdos P., Renyi A.. On the strength of connectedness of a random graph. Acta Math. Sci. Hungary, 1961, 12: 261-267.
[8] Milgram S.. The small world problem. Psychology Today, 1967, 2:60-67.
[9] Watts D. J., Strogatz S. H.. Collective dynamics of“small-world”networks. Nature, 1998, 393:440- 442.
[10] Barabàsi A .-L., Albet R.. Emergence of scaling in random networks. Science, 1999, 286:509-512.
[11] Albert R, Barabàsi A-L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74(1): 47-97.
[12] Barrat A, Weigt M.. On the properties of small world networks. Eur. Phys. J. B, 2000, 11:547-560.
[13] Newman M. E. J., Watts D. J.. Renormalization group analysis of the small-world network model. Phys. Lett. A, 1999, 263:341-346.
[14] Newman M. E. J., Watts D. J. Scaling and percolation in the small-world network model. Phys Rev. E, 1999, 60: 7332-7342.
[15] Newman M. E. J.. Models of the small-world. Journal of Statistical Physics, 2000, 101: 819-841.
[16] Goh K.-I., Kahng B., Kim D. .Universal Behavior of Load Distribution in Scale-Free Networks.Phys. Rev. Lett., 2001, 87: 278701-27874.
[17] Fan J, Wang X F. A wavelet of small-world networks. IEEE Trans. Circuits and Systems II, 2005,52(5):238-242.
[18] Barthelemy M., Amaral L. A. N.. Small-world networks: Evidence for acrossover picture. Phys Rev. Let., 1999, 82: 3180-3183.
[19] Cancho R. F., Janssen C., Sole R. V.. Topology of technology graphs: Small world paterns in electronic circuits. Phys. Rev. E, 2001, 64: 046119-046123.
[20] Ozana M.. Incipient spanning cluster on small-world networks. Europhys. Let., 2001, 55:762-766.
[21] Comellasa F., Sampels M.. Deterministic small-world networks. Physica A, 2002, 309: 231-235.
[22] Comellasa F., Ozbna J., Petersb J. G.. Deterministic small-world communication networks. Information Processing Leters, 2000, 76: 83-90.
[23] Monasson R.. Diffusion, localization and dispersion relations on‘small-world’lattices. Eur. Phys. J. B, 1999, 12:555-567.
[24] Arcangelis L. D., Herrmann H. J.. Self-organized criticality on small world networks. Physica A, 2002, 308: 545-549.
[25] Cosenza M. G, Tucci K.. Turbulence in small-world networks. Phys. Rev. E, 2002, 63:036223-036229.
[26] Hou Z., Xin H.. Oscillator death on small-world networks. Phys. Rev. E, 2003, 68:055103-055106.
[27] Gao Z., Hu B., Hu G.. Stochastic resonance of small-world networks. Phys. Rev. E, 2001, 65:016209-016212.
[28] Price D J . Networks of scientific papers. Science, 1965, 149(3683): 510-515.
[29] Bollobas B, Riordan O.. Mathematical results on scale-free random graphs. In Bornholdt, S, Schuster H G (ed.) Handbook of Graphs and Networks: From the Genome to the Internet, Berlin: Wiley-VCH, 2003, 1-34.
[30] Cohen R, Havlin S.. Scale-free networks are ultrasmall. Phys. Rev. Lett., 2003, 90: 058701-058704.
[31] Fronczak A, Fronczak P, Hilyst J A.. Mean-field theory for clustering coefficients in Barabàsi-Albert networks. Phys. Rev. E, 2003, 68:046126- 046129.
[32] Barabàsi A. -L., Albert R., Jeong H.. Scale-free characteristics of random networks: The topology of the World Wide Web. Physica A, 2000, 281: 9-77.
[33] Valverde S., Cancho R.F., Sole R. V.. Scale-free networks from optimal design. Eumphys Lett., 2002, 60:512-517.
[34] Caldarelli G., Capocci A., De Los Rios P. et al. Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett., 2002, 89: 258702-258705.
[35] Pastor-Satorras R., Vespignani A.. Epidemic spreading in scale-free networks. Phys. Rev. Lett., 2001, 86: 3200-3203.
[36] Pastor-Satorras R., Vespignani A.. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E, 2002, 65: 035108-035111.
[37] May R. M., Lloyd A. L.. Infection dynamics on scale-free networks. Phys. Rev. E, 2001, 64: 066112-066115.
[38] Lynch N. A.. Distributed Algorithms. Morgan Kaufmann Publishers, Inc,1997.
[39] DeGroot M. H.. Reaching a consensus. Journal of American Statistical Association, 1974, 69(345): 118-121.
[40] Benediktsson J. A., Swain P. H.. Consensus theoretic classification methods. IEEE Trans. on Systems, Man and Cybernetics, 1992, 22(4): 688-704.
[41] Saber R. O., Murray R. M.. Consensus protocols for networks of dynamic agents. Proc. 2003 ACC, 2003, 2: 951–956.
[42] Saber R. O., Murray R. M.. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Contr., 2004, 49( 9): 1520-1533.
[43] Saber R. O.. Ultrafast consensus in small-world network. Proc. ACC, Portland, OR, 2005, 4:2371-2378.
[44] Ren W., Beard R. W.. Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. on Automatic Control, 2005, 50(5): 655-660.
[45] Moreau L.. Stability of continuous-time distributed consensus algorithms. Proc. Of CDC, 2004, 4:3998-4003.
[46] Wang X. F., Chen G.. Synchronization in small-world dynamical networks. Int. J. Bifurcation and Chaos, 2002, 12 (1):187-192.
[47] Wang X. F., Chen G.. Synchronization in scale-free dynamical networks- robustness and fragility. IEEE Trans. CAS-I, 2002, 49: 54-62.
[48] Wang X. F.. Complex networks: Topology, dynamics and synchronization. Int. J. Bifurcation and Chaos, 2002, 12: 885-916.
[49] Wang X. F., Chen G.. Synchronization in complex dynamical networks. J. Systems Science and Complexity, 2003, 16:1-14.
[50] Li X., Wang X. F., Chen G.. Synchronization in complex dynamical networks and its applications. Conf. on Growing Networks and Graphics in Statistical Physics, Finance, Biology and Social Systems, Rome, Italy, 2003.
[51] Li X., Chen G.. Synchronization and desynchronization of complex dynamical networks-An engineering viewpoint. IEEE Trans. CAS-I, 2003, 50: 1381-1390.
[52] Fan J., Wang X. F., On Synchronization in scale-free dynamical networks. Physica A, 2005, 349:443-451.
[53] Lu J., Yu X., Chen G.. Chaos synchronization of general complex dynamical networks. Physica A, 2004, 334: 281-302.
[54] Pecora L. M., Carroll T. L.. Synchronization in chaotic systems. Phys. Rev. Let., 1990, 64: 821-825.
[55] Rosenblum M. G., Pikovsky A. S., Kurths J.. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett., 1997, 78: 4193-4196.
[56] Mainieri R., Rehacek J.. Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett., 1999, 82: 3042-3045.
[57] Voss H. U.. Anticipating chaotic synchronization. Phys. Rev. E, 2000, 61:5115-5119.
[58] Li C., Xu H., Liao X. et al.. Synchronization in small-world oscillator networks with coupling delays. Physica A, 2004, 335(3-4): 359-364.
[59] Gelover-Santiago A. L., Lima R., Matinez-Mekler G.. Synchronization and cluster periodic solutions in globally coupled maps. Physca A, 2000, 283: 131-135.
[60] Li C., Xu H., Liao X. et al.. Synchronization in coupled map lattices with small-world delayed interactions. Physica A, 2004, 335(3- 4): 365-370.
[61] Pikovsky A.S., Rosenblum M.G., Osipov G.V. et al. Phase synchronization of chaotic oscillators by external driving. Physica D, 1997, 104: 219-238.
[62] Blasius B., Huppert A., Stone L.. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature (London), 1999, 399: 354-359.
[63] Allaria E., Arechi F. T., Digarbo A. etal. Synchronization of homoclinic chaos. Phy. Rev. Lett., 2001, 86: 791-794.
[64] Taherion S., Lai Y.-C.. Experimental observation of lag synchronization in coupled chaotic systems. Int. J. Bifur. Chaos, 2000, 10: 2587-2594.
[65] Osipov G. V., A. Pikovsky S., Rosenblum M. G. et al. Phase synchronization effects in a lattice of nonidentical Rossler oscillators. Phys. Rev. E, 1997, 55: 2353-2361.
[66] Zheng Z., Hu G., Hu B.. Enhancement of phase synchronization throughasymmetric couplings. Phys. Rev. E, 2000, 62: 7501-7504.
[67] Ren Wei, Beard R. W., Atkins E. M.. A Survey of Consensus Problems in Multi-agent Coordination. 2005 ACC, Portland, OR, USA, 3:1859-1864, 2005.
[68]杨文,汪小帆,李翔,一致性问题综述,Proc. of the 25th CCC, 2006,中国哈尔滨,1491-1495.
[69] Moreau L.. Stability of multi-agent systems with time-dependent communication links. IEEE Trans. On Automatic Control, 2005, 50:169-182.
[70] Fang Lei, Antsaklis P.J., Information consensus of asynchronous discrete-time multi-agent systems.ACC, 2005, 3:1883-1888.
[71] Ren W., Beard R. W., McLain T. W.. Coordination variables and consensus building in multiple vehicle systems. in Cooperative Control (V. Kumar, N. E. Leonard, and A. S. Morse, eds.). Springer-Verlag Series: Lecture Notes in Control and Information Sciences, 2004, 309: 171–188.
[72] Lin Z., Francis B., Maggiore M.. Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. on Automatic Control, 2005, 50(1):121–127.
[73] Fax J. A., Murray R. M.. Information flow and cooperative control of vehicle formations. IEEE Trans. on Automatic Control, 2004, 49: 1465–1476.
[74] Gupta V., Hassibi B., Murray R.. Stability analysis of stochastically varying formations of dynamic agents. in Proc. of CDC, (Maui, Hawaii), 2003, 504–509.
[75] Lawton J. R., Beard R. W., Young B.. A decentralized approach to formation maneuvers. IEEE Transactions on Robotics and Automation, 2003, 19: 933–941.
[76] Glavaski S., Chaves M., Day R. et al. Vehicle networks: Achieving regular formation. in Proc. of ACC, (Denver, CO), 2003, 4095–4100.
[77] Vicsek T., Czirok A., Jacob E. B. et al. Novel type of phase transitions in asystem of self-driven particles. Phys. Rev. Lett., 1995, 75:1226-1229.
[78] Lawton J. R., Beard R. W., Synchronized multiple spacecraft rotations. Automatica, 2002, 38(8)1359–1364.
[79] Ren W., Beard R. W.. Decentralized scheme for spacecraft formation flying via the virtual structure approach. AIAA Journal of Guidance, Control, and Dynamics, 2004, 27:73–82.
[80] Bauso D., Giarr L., Pesenti R.. Attitude alignment of a team of UAVs under decentralized information structure. in IEEE Internation Conference on Control Applications, (Istanbul, Turkey), 2003, 1:486-491.
[81] Lin J., Morse A. S., B. Anderson D. O.. The multi-agent rendezvous problem. in Proc. of CDC, (Maui, Hawaii), 2003, 1508–1513.
[82] Kingston D. B., Ren W., Beard R. W.. Consensus algorithms are input-to-state stable. in Proc. of ACC, 2005, 3:1686-1960.
[83] Kauffman S. A.. Metabolic stability and epigenesis in randomly constructed genetic nets. J. of Theoretical Biology, 1969, 22(3):437–467.
[84] Newman M. E. J.. Scientific collaboration networks. I. network construction and fundamental results. Physical Review E, 2002, 64(1):0161311–0161318.
[85] Kopell N., Ermentrout G. B.. Symmetry and phaselocking in chains of weakly coupled oscillators. Communications in Pure and Appl. Math., 1986, 39:623– 660.
[86] Kuramoto Y.. Chemical oscillators, waves, and turbulance. Springer, Berlin, 1984.
[87] Mirollo R. E., Strogatz S. H.. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math., 1990, 50:1645–1662.
[88] Strogatz S. H.. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D, 2000, 143:1– 20.
[89] Winfree A. T.. Biological rythms and the behavior of populations of coupled oscillators. J. Theoretical Biology, 1967, 16:15–42.
[90] Cortes J., Martinez S., Karatas T. et al.. Coverage control for mobile sensing networks. The IEEE Trans. on Robotics and Automation, 2004, 20(2):243–255.
[91] Estrin D., Govindan R., Heidemann J. et al.. Next century challenges: scalable coordination in sensor networks. Proc. of Mobile Computing and Networking, 1999, 263–270.
[92] Mogilner A., Edelstein-Keshet L.. A non-local model for a swarm. J. Math. Biology, 1999, 38:534–570.
[93] Topaz C. M., Bertozzi A. L.. Swarming patterns in a two dimensional kinematic model for biological groups. Journal on Applied Mathematics, 2004, 65(1):152 -174.
[94] Beard R. W., Lawton J., Hadaegh F. Y.. A feedback architecture for formation control. IEEE Transactions on Control Systems Technology, 2001, 9:777-790.
[95] Kang W., Yeh H.-H.. Coordinated attitude control of multi-satellite systems. International Journal of Robust and Nonlinear Control, 2002, 12:185-205.
[96] Proud A. W., Pachter M., D’Azzo J. J.. Close formation flight control. in Proceedings of the AIAA Guidance, Navigation, arid Corntrol Conference and Exhibit, (Portland,OR), American Institute of Aeronautics and Astronautics, 1999. AIAA-99-4207:1231-1246.
[97] Stilwell D. J., Bishop B. E.. Platoons of underwater vehicles. IEEE Control Systems Magazine, 2000, 20:45-52.
[98] Horn R. A., Johnson C. R.. Matrix Analysis. Cambridge University Press 1987.
[99] Fiedler M.. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 1973, 23(98):298–305.
[100] Barabàsi A.-L., Albert R., Jeong H.. Mean-field theory for scale-free random networks. Physica A, 1999, 272: 173-187.
[101] Li X, Chen G. R.. A local-world evolving network model. Physica A, 2003, 328(1-2):274-286.
[102] Estrada E., Rodriguez-Velazquez J A..Subgraph centrality in complex networks. Phys. Rev. E. 2005, 71:056103-056111.
[103] Estrada E, Rodriguez-Velazquez J. A.. Spectral measure of bipartivity in complex networks. Phys. Rev. E, 2005, 72: 046105-046110.
[104] De Aguiar M. A. M., Bar-Yam Y.. Spectral analysis and the dynamic response of complex nctwodcs. Phys Rev E, 2005, 71: 016106-016110.
[105] Farkas I., Dcrenyi I., Jeong H. et al.. Networks in life scaling properties and eigenvalue spectra. Physica A, 2002, 314: 25-34.
[106] Holland J H., Adaptation in natural and artificial systems. AnnArbor, Michigan: University of Michigan Press,1975.
[107] Goldberg D E.. Genetic algorithm in search, optimization and machine learning. Reading MA: Addison-Wesley Publishing Company,1989.
[108]张晓缋,方浩,戴冠中.遗传算法的编码机制研究.信息与控制, 1997, 26(2): 134~139.
[109] Takashi Nishikawa, Adilson E. M., Lai Ying-Cheng et al. Smallest small-world network. Phys. Rev. E, 2002, 66:046139-046143.
[110] Dias M. B., Stentz A.. A Market Approach to Multirobot Coordination. Technical Report CMU-R I-TR-01-26. Robotics Institute, Carnegie Mellon University, 2001.
[111] Balch T., Arkin R. C.. Behavior-based Formation Control for Multirobot Teams. IEEE Trans on Robotics and Aut., 1998, 14 (6) : 1-15.
[112] Parker L. E.. Adaptive Heterogeneous Multi-robot Teams. Neurocomputing, 1999, 28: 75-92.
[113]曹志强,张斌,谭民.基于行为的多移动机器人实时队形保持.高技术通信,2001,10:74-77.
[114] Desai J. P., Ostrowski J. P., Kumar V.. Controlling formations of multiple mobile robots. in Proceedings of IEEE int. Conference on Robotics and Automation, Leuven, Belgium, 1998, 2864-2869.
[115] Fierro R., Das A. K., Kumar V. et al. Hybrid Control of formations of Robots. in Proceedings of IEEE int. Conference Robotics and Automation, Seoul, Korea, 2001, 157-162.
[116] Desai J. P., Ostrowski J. P., Kumar V.. Modeling and Control of Formation of Nonholonomic Mobile Robots. IEEE int. transaction on Robotics and Automation. 2001, 17(6):905-908.
[117] Tanner H. G., Pappas G. J., Kumar V.. Leader to formation stability. IEEE Trans on Robotics and Automation, 2004, 20(3):443-455.
[118] Tan K.-H., Lewis M.. Virtual structures for high-precision cooperative mobile robotic control. in proceedings of the 1996 IEE/RSJ International conference, 1996,1:132-139.
[119] Leonard N. E., Fiorelli E.. Virtual Leader, Artificial Potentials and Coordinated Control of Groups. in proceedings of the 40th IEEE conference on Decision and Control , Orlando, Florida USA, 2001, 3:2968-2973.
[120] Ren W., Beard R. W.. Formation feedback control for multiple spacecraft via virtual structures, IEE Proc Control Theory and Applications, 2004, 3:357-368.
[121] Anthony L. M., Tan K. H.. High. precision formation control of mobile robots using virtual structures autonomous. Autonomuous Robots, 1974, 387-403.
[122] Brett J Y., Beard R. W., Kelsey J. M.. A control scheme for improving multi-vehicle formaion maneuvers, American Control Conf., Arlington, 2001, 704-709.
[123] Reynolds C. W.. Flocks, herds, and schools: A distributed behavioral model. Computer Graphics, 1987, 21(4): 25-34.
[124] Jadbabaie A, Lin J, Morse A. S.. Coordination of groups of mobile autonomousagents using nearest neighbor rules. IEEE Trans on Automatic Control, 2003, 48(6): 988-1001.
[125] Balch T, Hybinette M. Social potentials for scalable multi-robot formations. Proc. IEEE Int Conf. on Robotics and Automation. San Fransisco, 2000, 1: 73-80.
[126] Kostelnik P, Samulka M, Janosik M. Scalable multi-robot formations using local sensing and communication. Proc. of the 3rd Int Workshop on Robot Motion and Control. Poznan, 2002, 319-324.
[127] Lawton J., Young B., Beard R.. A decentralized approach to elementary formation maneuvers. IEEE Int Conf on Robotics and Automation. San Fransico, 2000, 3: 2728-2733.
[128]董胜龙,陈卫东,席裕庚.多移动机器人编队的分布式控制系统.机器人, 2000, 22(6): 433-438.
[129] Desai J P. A graph theoretic approach for modeling mobile robot team formations . J of Robotic Systems, 2002, 511-525.
[130] Saber R. O., Murray R. M.. Flocking with obstacle avoidance: cooperation with limited communication in mobile networks. Proc. Of the IEEE Conf. on Decision and Control, 2003, 2022-2028.
[131] Huygenii G.. Horoloquim oscilatoriumm. France: Parisiism, 1673.
[132] Winfree A. T.. Geometry of biological time. New York: Springer-Verlag, 1990.
[133] Buck J B, Buck E. Mechanism of rhythmic synchronous flashing of fireflies. Science, 1968, 159: 1319-1327.
[134] Buck J B. Synchronous rhythmic flashing of fireflies. Quarterly Review of Biology, 1938, 13: 301-314.
[135] Buck J B. Synchronous rhythmic flashing of fireflies II. Quarterly Review of Biology, 1988, 63: 265-289.
[136] Kaneko K.. Coupled Map Lattices. Singapore: World Scientific, 1992.
[137] Chua L O.. CNN: A paradigm for Complexity, Singapore: World Scientific, 1993.
[138] Gade P M.. Synchronization of oscillators with random nonlocal connectivity. Phys. Rev. E, 1996, 54 (1) :64-70.
[139] Gade P M, Hu C-K.. Synchronization and coherence in thermodynamic coupled map lattices with intermediate-range coupling. Phys. Rev. E, 1999, 60 (4):4966-4969.
[140] Gade P M, Hu C-K.. Synchronous chaos in coupled map lattices with small-world interactions. Phys. Rev. E, 2000, 62 (5):6409-6413.
[141]赵明,汪秉宏,蒋品群,周涛.复杂网络上动力系统同步的研究进展.物理学进展,2005,25(3):273-295.
[142]赵明,周涛,陈关荣,汪秉宏.复杂网络上动力系统同步的研究进展Ⅱ——如何提高网络的同步能力.物理学进展,2006,25(3):273-295.
[143] Kang W., Xi N., Spaks A.. Theory and Applications of Formation Control in a Perceptive Referenced Frame. in Proceedings of IEEE int. Conference on Decision and Control, Sydney, Australia, 2000, 352-357.
[144] Hiroaki Yamaguchi, Tamio Arai, Gerardo Beni. A distributed control scheme for multiple robotic vehicles to make group formations. ELSEVIER, Robotics and Automations System , 2001, 36:125-147.
[145]廖晓昕,稳定性的理论、方法和应用,华中理工大学出版社,1998.
[146] Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents, part I: fixed topology. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway: IEEE, 2003. 2010-2015.
[147] Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents, part II: dynamic topology. Proceedings of the 42nd IEEE Conference on Decision and Control. Piscataway: IEEE, 2003,2016-2021.
[148] Tanner H G. Flocking with obstacle avoidance in switching networks ofinterconnected vehicles. Proceedings of the 2004 IEEE International Conference on Robotics and Automation. Piscataway: IEEE, 2004. 3006-3011.
[149]俞辉,王永骥.稳定的有领航者的多移动智能体群集运动控制.华中科技大学学报(自然科学版),2005,33(8):56-58.
[150] Saber R O. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Automat. Contr., 2006, 51(3):401-420.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |