图拉普拉斯视角下的多智能体系统分布式协调控制

HAN Zhi-min; LIN Zhi-yun; FU Min-yue; CHEN Zhi-yong

doi:10.1631/FITEE.1500118

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图拉普拉斯视角下的多智能体系统分布式协调控制

计算机与自动化 | Updated：2022-06-06

- 图拉普拉斯视角下的多智能体系统分布式协调控制
- Distributed coordination in multi-agent systems:a graph Laplacian perspective
- 信息与电子工程前沿（英文） 2015年16卷第6期页码：429-448
- Affiliations：
  
  1.State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  2.School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan NSW 2308, Australia
  3.State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  [ "Zhi-min HAN, E-mail: hanzhimin@zju.edu.cn" ]
  [ "", "Prof. Zhi-yun LIN, corresponding author of this invited review article, received his Bachelor degree in Electrical Engineering from Yanshan University, China, in 1998, Master degree in Electrical Engineering from Zhejiang University, China, in 2001, and PhD degree in Electrical and Computer Engineering from the University of Toronto, Canada, 2005. From 2005 to 2007, he was a Postdoctoral Research Associate in the Department of Electrical and Computer Engineering, University of Toronto, Canada. He joined the College of Electrical Engineering, Zhejiang University, China, in 2007. Currently, he is a Professor of Systems Control in the same college. He is also affiliated with the State Key Laboratory of Industrial Control Technology at Zhejiang University. He held visiting professor positions at several universities including the Australian National University (Australia), University of Cagliari (Italy), University of Newcastle (Australia), University of Technology Sydney (Australia), and Yale University (USA). His research interests focus on distributed control, estimation and optimization, coordinated and cooperative control of multi-agent systems, hybrid and switched system theory, and locomotion control of biped robots. He is a senior member of IEEE. He is currently an associate editor for Hybrid Systems: Nonlinear Analysis and International Journal of Wireless and Mobile Networking." ]
  [ "Min-yue FU, E-mail:minyue.fu@newcastle.edu.au" ]
  [ "Zhi-yong CHEN, E-mail: zhiyong.chen@newcastle.edu.au" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 61273113)
- DOI：10.1631/FITEE.1500118
  中图分类号： TP13
- 收稿：2015-04-13，
  
  修回：2015-05-15，
  
  纸质出版：2015-06
- Accepted：
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图拉普拉斯视角下的多智能体系统分布式协调控制[J]. 信息与电子工程前沿（英文）, 2015,16(6):429-448.

HAN Zhi-min, LIN Zhi-yun, FU Min-yue, et al. Distributed coordination in multi-agent systems:a graph Laplacian perspective[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(6): 429-448.
图拉普拉斯视角下的多智能体系统分布式协调控制[J]. 信息与电子工程前沿（英文）, 2015,16(6):429-448. DOI： 10.1631/FITEE.1500118.

HAN Zhi-min, LIN Zhi-yun, FU Min-yue, et al. Distributed coordination in multi-agent systems:a graph Laplacian perspective[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(6): 429-448. DOI： 10.1631/FITEE.1500118.

摘要

本综述从图拉普拉斯视角回顾多智能体系统分布式协调控制中的主要成果和进展。在过去几十年，多智能体分布式协调控制被系统与控制领域视为十分具有吸引力的一个课题。利用多智能体分布式协调控制可以解决分布式一致性控制、编队控制、传感器定位、分布式最优化等问题。除回顾广泛的多智能体分布式协调控制文献外，本文还提供一个全新的角度，即图拉普拉斯，对众多的分布式协调控制基于基本机制进行分类。对于不同类型的图拉普拉斯，分别总结其内在协调特性以及相应的研究课题。文章最后着重介绍具有发展前景的研究方向以及对未来有重大研究意义的开放性问题。

Abstract

This paper reviews some main results and progress in distributed multi-agent coordination from a graph Laplacian perspective. Distributed multi-agent coordination has been a very active subject studied extensively by the systems and control community in last decades

including distributed consensus

formation control

sensor localization

distributed optimization

etc. The aim of this paper is to provide both a comprehensive survey of existing literature in distributed multi-agent coordination and a new perspective in terms of graph Laplacian to categorize the fundamental mechanisms for distributed coordination. For different types of graph Laplacians

we summarize their inherent coordination features and specific research issues. This paper also highlights several promising research directions along with some open problems that are deemed important for future study.

关键词

Keywords

references

C. Altafini . Consensus problems on networks with antagonistic interactions . IEEE Trans. Automat. Contr. , 2013 . 58 ( 4 ): 935 - 946 . DOI: 10.1109/TAC.2012.2224251 http://doi.org/10.1109/TAC.2012.2224251 .

B.D.O. Anderson , C. Yu , B. Fidan , 等 . Rigid graph control architectures for autonomous formations . IEEE Contr. Syst. , 2008 . 28 ( 6 ): 48 - 63 . DOI: 10.1109/MCS.2008.929280 http://doi.org/10.1109/MCS.2008.929280 .

P. Bliman , G. Ferrari-Trecate . Average consensus problems in networks of agents with delayed communications . Automatica , 2008 . 44 ( 8 ): 1985 - 1995 . DOI: 10.1016/j.automatica.2007.12.010 http://doi.org/10.1016/j.automatica.2007.12.010 .

V.D. Blondel , J.M. Hendrickx , A. Olshevsky , 等 . Convergence in multiagent coordination, consensus, and flocking . Proc. 44th IEEE Conf. on Decision and Control and European Control Conf. , 2005 . p.2996 - 3000 . DOI: 10.1109/CDC.2005.1582620 http://doi.org/10.1109/CDC.2005.1582620 .

S. Boyd . Convex optimization of graph Laplacian eigenvalues . Proc. Int. Congress of Mathematicians , 2006 . p.1311 - 1320 . .

S. Boyd , P. Diaconis , P. Parrilo , 等 . Fastest mixing Markov chain on graphs with symmetries . SIAM J. Optim. , 2009 . 20 ( 2 ): 792 - 819 . DOI: 10.1137/070689413 http://doi.org/10.1137/070689413 .

F. Bullo , J. Cortés , S. Martínez . Distributed Control of Robotic Networks , : USA Princeton University Press , 2009 .

K. Cai , H. Ishii . Average consensus on general strongly connected digraphs . Automatica , 2012 . 48 ( 11 ): 2750 - 2761 . DOI: 10.1016/j.automatica.2012.08.003 http://doi.org/10.1016/j.automatica.2012.08.003 .

K. Cai , H. Ishii . Average consensus on arbitrary strongly connected digraphs with time-varying topologies . IEEE Trans. Automat. Contr. , 2014 . 59 ( 4 ): 1066 - 1071 . DOI: 10.1109/TAC.2014.2305952 http://doi.org/10.1109/TAC.2014.2305952 .

L. Cao , Y. Zheng , Q. Zhou . A necessary and sufficient condition for consensus of continuous-time agents over undirected time-varying networks . IEEE Trans. Automat. Contr. , 2011 . 56 ( 8 ): 1915 - 1920 . DOI: 10.1109/TAC.2011.2157393 http://doi.org/10.1109/TAC.2011.2157393 .

D.W. Casbeer , R. Beard , A.L. Swindlehurst . Discrete double integrator consensus . Proc. 47th IEEE Conf. on Decision and Control , 2008 . p.2264 - 2269 . DOI: 10.1109/CDC.2008.4739168 http://doi.org/10.1109/CDC.2008.4739168 .

J. Chen , C. Wang , Y. Sun , 等 . Semi-supervised Laplacian regularized least squares algorithm for localization in wireless sensor networks . Comput. Netw. , 2011 . 55 ( 10 ): 2481 - 2491 . DOI: 10.1016/j.comnet.2011.04.010 http://doi.org/10.1016/j.comnet.2011.04.010 .

J. Cortés . Distributed algorithms for reaching consensus on general functions . Automatica , 2008 . 44 ( 3 ): 726 - 737 . DOI: 10.1016/j.automatica.2007.07.022 http://doi.org/10.1016/j.automatica.2007.07.022 .

J. Cortés . Global and robust formation-shape stabilization of relative sensing networks . Automatica , 2009 . 45 ( 12 ): 2754 - 2762 . DOI: 10.1016/j.automatica.2009.09.019 http://doi.org/10.1016/j.automatica.2009.09.019 .

N.M.M. de Abreu . Old and new results on algebraic connectivity of graphs . Linear Algebra Appl. , 2007 . 423 ( 1 ): 53 - 73 . DOI: 10.1016/j.laa.2006.08.017 http://doi.org/10.1016/j.laa.2006.08.017 .

M.H. Degroot . Reaching a consensus . J. Am. Statist. Assoc. , 1974 . 69 ( 345 ): 118 - 121 . .

Y. Diao , Z. Lin , M. Fu , 等 . Localizability and distributed localization of sensor networks using relative position measurements . Proc. 13th IFAC Symp. on Large Scale Complex Systems: Theory and Applications , 2013 . p.1 - 6 . DOI: 10.3182/20130708-3-CN-2036.00069 http://doi.org/10.3182/20130708-3-CN-2036.00069 .

Y. Diao , Z. Lin , M. Fu . A barycentric coordinate based distributed localization algorithm for sensor networks . IEEE Trans. Signal Process. , 2014 . 62 ( 18 ): 4760 - 4771 . DOI: 10.1109/TSP.2014.2339797 http://doi.org/10.1109/TSP.2014.2339797 .

W. Ding , G. Yan , Z. Lin . Collective motion and formations under pursuit strategies on directed acyclic graphs . Automatica , 2010 . 46 ( 1 ): 174 - 181 . DOI: 10.1016/j.automatica.2009.10.025 http://doi.org/10.1016/j.automatica.2009.10.025 .

W. Ding , G. Yan , Z. Lin . Pursuit formations with dynamic control gains . Int. J. Robust Nonlinear Contr. , 2012 . 22 ( 3 ): 300 - 317 . DOI: 10.1002/rnc.1692 http://doi.org/10.1002/rnc.1692 .

A.D. Dominguez-Garcia , S.T. Cady , C.N. Hadjicostis . Decentralized optimal dispatch of distributed energy resources . Proc. IEEE 51st Annual Conf. on Decision and Control , 2012 . p.3688 - 3693 . DOI: 10.1109/CDC.2012.6426665 http://doi.org/10.1109/CDC.2012.6426665 .

F. Dörfler , F. Bullo . Synchronization in complex networks of phase oscillators: a survey . Automatica , 2014 . 50 ( 6 ): 1539 - 1564 . DOI: 10.1016/j.automatica.2014.04.012 http://doi.org/10.1016/j.automatica.2014.04.012 .

D. Easley , J. Kleinberg . Networks, Crowds, and Markets: Reasoning about a Highly Connected World , : UK Cambridge University Press , 2010 .

M.P. Fanti , A.M. Mangini , F. Mazzia , 等 . A new class of consensus protocols for agent networks with discrete time dynamics . Automatica , 2015 . 54 1 - 7 . DOI: 10.1016/j.automatica.2015.01.025 http://doi.org/10.1016/j.automatica.2015.01.025 .

A. Ghosh , S. Boyd , A. Saberi . Minimizing effective resistance of a graph . SIAM Rev. , 2008 . 50 ( 1 ): 37 - 66 . DOI: 10.1137/050645452 http://doi.org/10.1137/050645452 .

C. Godsil , G. Royle . Algebraic Graph Theory , : New York, USA Springer , 2001 .

D.K. Goldenberg , P. Bihler , M. Cao , 等 . Localization in sparse networks using sweeps . Proc. 12th Annual Int. Conf. on Mobile Computing and Networking , 2006 . p.110 - 121 . DOI: 10.1145/1161089.1161103 http://doi.org/10.1145/1161089.1161103 .

S.J. Gortler , A.D. Healy , D.P. Thurston . Characterizing generic global rigidity . Am. J. Math. , 2010 . 132 ( 4 ): 897 - 939 . DOI: 10.1353/ajm.0.0132 http://doi.org/10.1353/ajm.0.0132 .

T. Han , Z. Lin , M. Fu . Formation merging control in 3D under directed and switching topologies . Proc. 19th IFAC World Congress , 2014a . p.10036 - 10041 . DOI: 10.3182/20140824-6-ZA-1003.02182 http://doi.org/10.3182/20140824-6-ZA-1003.02182 .

T. Han , Z. Lin , W. Xu , 等 . Three-dimensional formation merging control of second-order agents under directed and switching topologies . Proc. 11th IEEE Int. Conf. on Control and Automation , 2014b . p.225 - 230 . DOI: 10.1109/ICCA.2014.6870924 http://doi.org/10.1109/ICCA.2014.6870924 .

Y. Han , W. Lu , T. Chen . Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs . IEEE Trans. Neur. Netw. Learn. Syst. , 2013 . 24 ( 4 ): 566 - 578 . DOI: 10.1109/TNNLS.2013.2237786 http://doi.org/10.1109/TNNLS.2013.2237786 .

Z. Han , L. Wang , Z. Lin , 等 . Double-graph formation control for co-leader vehicle networks . Proc. 24th Chinese Control and Decision Conf. , 2012 . p.158 - 163 . DOI: 10.1109/CCDC.2012.6244024 http://doi.org/10.1109/CCDC.2012.6244024 .

Z. Han , L. Wang , Z. Lin . Local formation control strategies with undetermined and determined formation scales for co-leader vehicle networks . Proc. IEEE 52nd Annual Conf. on Decision and Control , 2013 . p.7339 - 7344 . DOI: 10.1109/CDC.2013.6761054 http://doi.org/10.1109/CDC.2013.6761054 .

Z. Han , Z. Lin , M. Fu . A fully distributed approach to formation maneuvering control of multi-agent systems . Proc. IEEE 53rd Annual Conf. on Decision and Control , 2014 . p.6185 - 6190 . DOI: 10.1109/CDC.2014.7040358 http://doi.org/10.1109/CDC.2014.7040358 .

C. He , Z. Feng , Z. Ren . Flocking of multi-agents based on consensus protocol and pinning control . Proc. 10th World Congress on Intelligent Control and Automation , 2012 . p.1311 - 1316 . DOI: 10.1109/WCICA.2012.6358083 http://doi.org/10.1109/WCICA.2012.6358083 .

J.M. Hendrickx , J.N. Tsitsiklis . Convergence of type-symmetric and cut-balanced consensus seeking systems . IEEE Trans. Automat. Contr. , 2013 . 58 ( 1 ): 214 - 218 . DOI: 10.1109/TAC.2012.2203214 http://doi.org/10.1109/TAC.2012.2203214 .

Y. Hong , J. Hu , L. Gao . Tracking control for multi-agent consensus with an active leader and variable topology . Automatica , 2006 . 42 ( 7 ): 1177 - 1182 . DOI: 10.1016/j.automatica.2006.02.013 http://doi.org/10.1016/j.automatica.2006.02.013 .

H. Huang , Q. Wu . $H_\infty$ control of distributed multi-agent formation systems with Toeplitz-based consensus algorithms . Proc. American Control Conf. , 2010 . p.6840 - 6845 . DOI: 10.1109/ACC.2010.5531579 http://doi.org/10.1109/ACC.2010.5531579 .

K. Hwang , S. Tan , C. Chen . Cooperative strategy based on adaptive Q-learning for robot soccer systems . IEEE Trans. Fuzzy Syst. , 2004 . 12 ( 4 ): 569 - 576 . DOI: 10.1109/TFUZZ.2004.832523 http://doi.org/10.1109/TFUZZ.2004.832523 .

A. Jadbabaie , J. Lin , A.S. Morse . Coordination of groups of mobile autonomous agents using nearest neighbor rules . IEEE Trans. Automat. Contr. , 2003 . 48 ( 6 ): 988 - 1001 . DOI: 10.1109/TAC.2003.812781 http://doi.org/10.1109/TAC.2003.812781 .

H. Jiang , L. Zhang , S. Guo . Cluster anti-consensus in directed networks of multi-agents based on the Q-theory . J. Franklin Inst. , 2014 . 351 ( 10 ): 4802 - 4816 . DOI: 10.1016/j.jfranklin.2014.08.002 http://doi.org/10.1016/j.jfranklin.2014.08.002 .

S. Kar , G. Hug . Distributed robust economic dispatch in power systems: a consensus + innovations approach . Proc. IEEE Power and Energy Society General Meeting , 2012 . p.1 - 8 . DOI: 10.1109/PESGM.2012.6345156 http://doi.org/10.1109/PESGM.2012.6345156 .

U.A. Khan , S. Kar , J.M.F. Moura . Distributed sensor localization in random environments using minimal number of anchor nodes . IEEE Trans. Signal Process. , 2009 . 57 ( 5 ): 2000 - 2016 . DOI: 10.1109/TSP.2009.2014812 http://doi.org/10.1109/TSP.2009.2014812 .

D.B. Kingston , R.W. Beard . Discrete-time average-consensus under switching network topologies . Proc. American Control Conf. , 2006 . p.3551 - 3556 . DOI: 10.1109/ACC.2006.1657268 http://doi.org/10.1109/ACC.2006.1657268 .

J. Kunegis , S. Schmidt , A. Lommatzsch . Spectral analysis of signed graphs for clustering, prediction and visualization . SIAM , 2010 . 10 559 - 570 . .

Y. Kuriki , T. Namerikawa . Consensus-based cooperative formation control with collision avoidance for a multi-UAV system . Proc. American Control Conf. , 2014 . p.2077 - 2082 . DOI: 10.1109/ACC.2014.6858777 http://doi.org/10.1109/ACC.2014.6858777 .

H. Lakshmanan , D.P. de Farias . Decentralized resource allocation in dynamic networks of agents . SIAM J. Optim. , 2008 . 19 ( 2 ): 911 - 940 . DOI: 10.1137/060662228 http://doi.org/10.1137/060662228 .

N.E. Leonard , D.A. Paley , F. Lekien , 等 . Collective motion, sensor networks, and ocean sampling . Proc. IEEE , 2007 . 95 ( 1 ): 48 - 74 . DOI: 10.1109/JPROC.2006.887295 http://doi.org/10.1109/JPROC.2006.887295 .

S. Li , H. Du , X. Lin . Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics . Automatica , 2011 . 47 ( 8 ): 1706 - 1712 . DOI: 10.1016/j.automatica.2011.02.045 http://doi.org/10.1016/j.automatica.2011.02.045 .

Z. Li , Y. Jia , J. Du , 等 . Flocking for multi-agent systems with switching topology in a noisy environment . Proc. American Control Conf. , 2008 . p.111 - 116 . DOI: 10.1109/ACC.2008.4586476 http://doi.org/10.1109/ACC.2008.4586476 .

Z. Lin . Distributed Control and Analysis of Coupled Cell Systems , : Germany VDM-Verlag , 2008 .

Z. Lin , M. Broucke , B. Francis . Local control strategies for groups of mobile autonomous agents . IEEE Trans. Automat. Contr. , 2004 . 49 ( 4 ): 622 - 629 . DOI: 10.1109/TAC.2004.825639 http://doi.org/10.1109/TAC.2004.825639 .

Z. Lin , B. Francis , M. Maggiore . Necessary and sufficient graphical conditions for formation control of unicycles . IEEE Trans. Automat. Contr. , 2005 . 50 ( 1 ): 121 - 127 . DOI: 10.1109/TAC.2004.841121 http://doi.org/10.1109/TAC.2004.841121 .

Z. Lin , B. Francis , M. Maggiore . State agreement for continuous-time coupled nonlinear systems . SIAM J. Contr. Optim. , 2007 . 46 ( 1 ): 288 - 307 . DOI: 10.1137/050626405 http://doi.org/10.1137/050626405 .

Z. Lin , Z. Chen , M. Fu . A linear control approach to distributed multi-agent formations in $d$-dimensional space . Proc. IEEE 52nd Annual Conf. on Decision and Control , 2013a . p.6049 - 6054 . DOI: 10.1109/CDC.2013.6760845 http://doi.org/10.1109/CDC.2013.6760845 .

Z. Lin , W. Ding , G. Yan , 等 . Leader-follower formation via complex Laplacian . Automatica , 2013b . 49 ( 6 ): 1900 - 1906 . DOI: 10.1016/j.automatica.2013.02.055 http://doi.org/10.1016/j.automatica.2013.02.055 .

Z. Lin , L. Wang , Z. Han , 等 . Distributed formation control of multi-agent systems using complex Laplacian . IEEE Trans. Automat. Contr. , 2014 . 59 ( 7 ): 1765 - 1777 . DOI: 10.1109/TAC.2014.2309031 http://doi.org/10.1109/TAC.2014.2309031 .

Z. Lin , M. Fu , Y. Diao . Distributed self localization for relative position sensing networks in 2D space . IEEE Trans. Signal Process., in press , 2015 . DOI: 10.1109/TSP.2015.2432739 http://doi.org/10.1109/TSP.2015.2432739 .

X. Liu , T. Chen . Cluster synchronization in directed networks via intermittent pinning control . IEEE Trans. Neur. Netw. , 2011 . 22 ( 7 ): 1009 - 1020 . DOI: 10.1109/TNN.2011.2139224 http://doi.org/10.1109/TNN.2011.2139224 .

W. Lu , B. Liu , T. Chen . Cluster synchronization in networks of coupled nonidentical dynamical systems . Chaos , 2010 . 20 ( 1 ): Article 013120 DOI: 10.1063/1.3329367 http://doi.org/10.1063/1.3329367 .

X. Lu , F. Austin , S. Chen . Cluster consensus of nonlinearly coupled multi-agent systems in directed graphs . Chin. Phys. Lett. , 2010a . 27 ( 5 ): Article 050503 DOI: 10.1088/0256-307X/27/5/050503 http://doi.org/10.1088/0256-307X/27/5/050503 .

X. Lu , F. Austin , S. Chen . Cluster consensus of second-order multi-agent systems via pinning control . Chin. Phys. B , 2010b . 19 ( 12 ): Article 120506 DOI: 10.1088/1674-1056/19/12/120506 http://doi.org/10.1088/1674-1056/19/12/120506 .

S. Martin . Multi-agent flocking under topological interactions . Syst. Contr. Lett. , 2014 . 69 53 - 61 . DOI: 10.1016/j.sysconle.2014.04.004 http://doi.org/10.1016/j.sysconle.2014.04.004 .

M. Mesbahi , M. Egerstedt . Graph Theoretic Methods for Multagent Networks , : USA Princeton University Press , 2010 .

F. Morbidi . The deformed consensus protocol . Automatica , 2013 . 49 ( 10 ): 3049 - 3055 . DOI: 10.1016/j.automatica.2013.07.006 http://doi.org/10.1016/j.automatica.2013.07.006 .

L. Moreau . Stability of multiagent systems with time-dependent communication links . IEEE Trans. Automat. Contr. , 2005 . 50 ( 2 ): 169 - 182 . DOI: 10.1109/TAC.2004.841888 http://doi.org/10.1109/TAC.2004.841888 .

N. Moshtagh , A. Jadbabaie . Distributed geodesic control laws for flocking of nonholonomic agents . IEEE Trans. Automat. Contr. , 2007 . 52 ( 4 ): 681 - 686 . DOI: 10.1109/TAC.2007.894528 http://doi.org/10.1109/TAC.2007.894528 .

N. Moshtagh , A. Jadbabaie , K. Daniilidis . Vision-based control laws for distributed flocking of nonholonomic agents . Proc. IEEE Int. Conf. on Robotics and Automation , 2006 . p.2769 - 2774 . DOI: 10.1109/ROBOT.2006.1642120 http://doi.org/10.1109/ROBOT.2006.1642120 .

R.M. Murray . Recent research in cooperative control of multivehicle systems . J. Dynam. Syst. Meas. Contr. , 2007 . 129 ( 5 ): 571 - 583 . DOI: 10.1115/1.2766721 http://doi.org/10.1115/1.2766721 .

A. Nedic , A. Ozdaglar , P.A. Parrilo . Constrained consensus and optimization in multi-agent networks . IEEE Trans. Automat. Contr. , 2010 . 55 ( 4 ): 922 - 938 . DOI: 10.1109/TAC.2010.2041686 http://doi.org/10.1109/TAC.2010.2041686 .

K. Oh , H.S. Ahn . Formation control and network localization via orientation alignment . IEEE Trans. Automat. Contr. , 2014 . 59 ( 2 ): 540 - 545 . DOI: 10.1109/TAC.2013.2272972 http://doi.org/10.1109/TAC.2013.2272972 .

K. Oh , F. Lashhab , K.L. Moore , 等 . Consensus of positive real systems cascaded with a single integrator . Int. J. Robust Nonlinear Contr. , 2015a . 25 ( 3 ): 418 - 429 . DOI: 10.1002/rnc.3093 http://doi.org/10.1002/rnc.3093 .

K. Oh , M.C. Park , H.S. Ahn . A survey of multi-agent formation control . Automatica , 2015b . 53 424 - 440 . DOI: 10.1016/j.automatica.2014.10.022 http://doi.org/10.1016/j.automatica.2014.10.022 .

A. Okubo . Dynamical aspects of animal grouping: swarms, schools, flocks, and herds . Adv. Biophys. , 1986 . 22 1 - 94 . DOI: 10.1016/0065-227X(86)90003-1 http://doi.org/10.1016/0065-227X(86)90003-1 .

R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays . IEEE Trans. Automat. Contr. , 2004 . 49 ( 9 ): 1520 - 1533 . DOI: 10.1109/TAC.2004.834113 http://doi.org/10.1109/TAC.2004.834113 .

R. Olfati-Saber , J.A. Fax , R.M. Murray . Consensus and cooperation in networked multi-agent systems . Proc. IEEE , 2007 . 95 ( 1 ): 215 - 233 . DOI: 10.1109/JPROC.2006.887293 http://doi.org/10.1109/JPROC.2006.887293 .

K.M. Passino . Biomimicry of bacterial foraging for distributed optimization and control . IEEE Contr. Syst. , 2002 . 22 ( 3 ): 52 - 67 . DOI: 10.1109/MCS.2002.1004010 http://doi.org/10.1109/MCS.2002.1004010 .

A. Proskurnikov . Consensus in switching symmetric networks of first-order agents with delayed relative measurements . Proc. IEEE 52nd Annual Conf. on Decision and Control , 2013 . p.917 - 921 . DOI: 10.1109/CDC.2013.6759999 http://doi.org/10.1109/CDC.2013.6759999 .

J. Qin , C. Yu . Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition . Automatica , 2013 . 49 ( 9 ): 2898 - 2905 . DOI: 10.1016/j.automatica.2013.06.017 http://doi.org/10.1016/j.automatica.2013.06.017 .

J. Qin , W.X. Zheng , H. Gao . Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology . Automatica , 2011 . 47 ( 9 ): 1983 - 1991 . DOI: 10.1016/j.automatica.2011.05.014 http://doi.org/10.1016/j.automatica.2011.05.014 .

Z. Qu . Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles , : UK Springer-Verlag, London , 2009 .

W. Ren . Consensus strategies for cooperative control of vehicle formations . IET Contr. Theory Appl. , 2007 . 1 ( 2 ): 505 - 512 . DOI: 10.1049/iet-cta:20050401 http://doi.org/10.1049/iet-cta:20050401 .

W. Ren . On consensus algorithms for double-integrator dynamics . IEEE Trans. Automat. Contr. , 2008 . 53 ( 6 ): 1503 - 1509 . DOI: 10.1109/TAC.2008.924961 http://doi.org/10.1109/TAC.2008.924961 .

W. Ren , R. Beard . Consensus of information under dynamically changing interaction topologies . Proc. American Control Conf. , 2004 . p.4939 - 4944 . .

W. Ren , R. Beard . Consensus seeking in multiagent systems under dynamically changing interaction topologies . IEEE Trans. Automat. Contr. , 2005 . 50 ( 5 ): 655 - 661 . DOI: 10.1109/TAC.2005.846556 http://doi.org/10.1109/TAC.2005.846556 .

W. Ren , R. Beard . Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications , : UK Springer, London , 2008 .

W. Ren , Y. Cao . Convergence of sampled-data consensus algorithms for double-integrator dynamics . Proc. 47th IEEE Conf. on Decision and Control , 2008 . p.3965 - 3970 . DOI: 10.1109/CDC.2008.4738652 http://doi.org/10.1109/CDC.2008.4738652 .

W. Ren , Y. Cao . Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues , : UK Springer-Verlag, London , 2011 .

W. Ren , R. Beard , E.M. Atkins . Information consensus in multivehicle cooperative control . IEEE Contr. Syst. , 2007 . 27 ( 2 ): 71 - 82 . DOI: 10.1109/MCS.2007.338264 http://doi.org/10.1109/MCS.2007.338264 .

C.W. Reynolds . Flocks, herds and schools: a distributed behavioral model . ACM SIGGRAPH Comput. Graph. , 1987 . 21 ( 4 ): 25 - 34 . DOI: 10.1145/37402.37406 http://doi.org/10.1145/37402.37406 .

S.H. Semnani , O.A. Basir . Semi-flocking algorithm for motion control of mobile sensors in large-scale surveillance systems . IEEE Trans. Cybern. , 2015 . 45 ( 1 ): 129 - 137 . DOI: 10.1109/TCYB.2014.2328659 http://doi.org/10.1109/TCYB.2014.2328659 .

S.S. Stanković , M.S. Stankoviá , D.M. Stipanović . Consensus based overlapping decentralized estimation with missing observations and communication faults . Automatica , 2009 . 45 ( 6 ): 1397 - 1406 . DOI: 10.1016/j.automatica.2009.02.014 http://doi.org/10.1016/j.automatica.2009.02.014 .

K. Sugihara , I. Suzuki . Distributed motion coordination of multiple mobile robots . Proc. 5th IEEE Int. Symp. on Intelligent Control , 1990 . p.138 - 143 . DOI: 10.1109/ISIC.1990.128452 http://doi.org/10.1109/ISIC.1990.128452 .

J. Sun , S. Boyd , L. Xiao , 等 . The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem . SIAM Rev. , 2006 . 48 ( 4 ): 681 - 699 . DOI: 10.1137/S0036144504443821 http://doi.org/10.1137/S0036144504443821 .

A. Tahbaz-Salehi , A. Jadbabaie . A necessary and sufficient condition for consensus over random networks . IEEE Trans. Automat. Contr. , 2008 . 53 ( 3 ): 791 - 795 . DOI: 10.1109/TAC.2008.917743 http://doi.org/10.1109/TAC.2008.917743 .

Y. Tian , C. Liu . Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations . Automatica , 2009 . 45 ( 5 ): 1347 - 1353 . DOI: 10.1016/j.automatica.2009.01.009 http://doi.org/10.1016/j.automatica.2009.01.009 .

J.N. Tsitsiklis . Problems in Decentralized Decision Making and Computation . PhD Thesis, Massachusetts Institute of Technology, USA , 1984 .

J.N. Tsitsiklis , D.P. Bertsekas , M. Athans . Distributed asynchronous deterministic and stochastic gradient optimization algorithms . IEEE Trans. Automat. Contr. , 1986 . 31 ( 9 ): 803 - 812 . DOI: 10.1109/TAC.1986.1104412 http://doi.org/10.1109/TAC.1986.1104412 .

C. Wang , J. Chen , Y. Sun , 等 . A graph embedding method for wireless sensor networks localization . Proc. IEEE Global Telecommunications Conf. , 2009 . p.1 - 6 . DOI: 10.1109/GLOCOM.2009.5425241 http://doi.org/10.1109/GLOCOM.2009.5425241 .

J. Wang , N. Elia . Consensus over networks with dynamic channels . Int. J. Syst. Contr. Commun. , 2010 . 2 ( 1 ): 275 - 297 . DOI: 10.1504/IJSCC.2010.031167 http://doi.org/10.1504/IJSCC.2010.031167 .

L. Wang , Z. Han , Z. Lin . Formation control of directed multi-agent networks based on complex Laplacian . Proc. IEEE 51st Annual Conf. on Decision and Control , 2012a . p.5292 - 5297 . DOI: 10.1109/CDC.2012.6426199 http://doi.org/10.1109/CDC.2012.6426199 .

L. Wang , Z. Han , Z. Lin , 等 . Complex Laplacian and pattern formation in multi-agent systems . Proc. 24th Chinese Control and Decision Conf. , 2012b . p.628 - 633 . DOI: 10.1109/CCDC.2012.6244096 http://doi.org/10.1109/CCDC.2012.6244096 .

L. Wang , Z. Han , Z. Lin . Realizability of similar formation and local control of directed multi-agent networks in discrete-time . Proc. IEEE 52nd Annual Conf. on Decision and Control , 2013 . p.6037 - 6042 . DOI: 10.1109/CDC.2013.6760843 http://doi.org/10.1109/CDC.2013.6760843 .

L. Wang , Z. Han , Z. Lin , 等 . A linear approach to formation control under directed and switching topologies . Proc. IEEE Int. Conf. on Robotics and Automation , 2014a . p.3595 - 3600 . DOI: 10.1109/ICRA.2014.6907378 http://doi.org/10.1109/ICRA.2014.6907378 .

L. Wang , Z. Lin , M. Fu . Affine formation of multi-agent systems over directed graphs . Proc. IEEE 53rd Annual Conf. on Decision and Control , 2014b . p.3017 - 3022 . DOI: 10.1109/CDC.2014.7039853 http://doi.org/10.1109/CDC.2014.7039853 .

W. Wang , H. Peng . Flocking control with communication noise based on second-order distributed consensus algorithm . Proc. IEEE Power Engineering and Automation Conf. , 2012 . p.1 - 4 . DOI: 10.1109/PEAM.2012.6612493 http://doi.org/10.1109/PEAM.2012.6612493 .

S. Wasserman , K. Faust . Social Network Analysis Methods and Applications , : UK Cambridge University Press , 1994 .

J. Wei , H. Fang . Multi-agent consensus with time-varying delays and switching topologies . J. Syst. Eng. Electron. , 2014 . 25 ( 3 ): 489 - 495 . DOI: 10.1109/JSEE.2014.00056 http://doi.org/10.1109/JSEE.2014.00056 .

G. Weiss . Multiagent Systems, a Modern Approach to Distributed Artificial Intelligence , : USA MIT Press , 1999 .

W. Wu , T. Chen . Partial synchronization in linearly and symmetrically coupled ordinary differential systems . Phys. D , 2009 . 238 ( 4 ): 355 - 364 . DOI: 10.1016/j.physd.2008.10.012 http://doi.org/10.1016/j.physd.2008.10.012 .

W. Wu , W. Zhou , T. Chen . Cluster synchronization of linearly coupled complex networks under pinning control . IEEE Trans. Circ. Syst. I , 2009 . 56 ( 4 ): 829 - 839 . DOI: 10.1109/TCSI.2008.2003373 http://doi.org/10.1109/TCSI.2008.2003373 .

W. Xia , M. Cao . Clustering in diffusively coupled networks . Automatica , 2011 . 47 ( 11 ): 2395 - 2405 . DOI: 10.1016/j.automatica.2011.08.043 http://doi.org/10.1016/j.automatica.2011.08.043 .

L. Xiao , S. Boyd . Fast linear iterations for distributed averaging . Syst. Contr. Lett. , 2004 . 53 ( 1 ): 65 - 78 . DOI: 10.1016/j.sysconle.2004.02.022 http://doi.org/10.1016/j.sysconle.2004.02.022 .

L. Xiao , S. Boyd . Optimal scaling of a gradient method for distributed resource allocation . J. Optim. Theory Appl. , 2006 . 129 ( 3 ): 469 - 488 . DOI: 10.1007/s10957-006-9080-1 http://doi.org/10.1007/s10957-006-9080-1 .

L. Xiao , S. Boyd , S. Kim . Distributed average consensus with least-mean-square deviation . J. Parall. Distr. Comput. , 2007 . 67 ( 1 ): 33 - 46 . DOI: 10.1016/j.jpdc.2006.08.010 http://doi.org/10.1016/j.jpdc.2006.08.010 .

H. Xing , Y. Mou , M. Fu , 等 . Distributed bisection method for economic power dispatch in smart grid . IEEE Trans. Power Syst., in press , 2015 . DOI: 10.1109/TPWRS.2014.2376935 http://doi.org/10.1109/TPWRS.2014.2376935 .

Y. Xu , T. Han , K. Cai , 等 . A fully distributed approach to resource allocation problem under directed and switching topologies . Proc. 10th Asian Control Conf., in press , 2015 .

S. Yang , S. Tan , J. Xu . Consensus based approach for economic dispatch problem in a smart grid . IEEE Trans. Power Syst. , 2013 . 28 ( 4 ): 4416 - 4426 . DOI: 10.1109/TPWRS.2013.2271640 http://doi.org/10.1109/TPWRS.2013.2271640 .

J. Yu , L. Wang . Group consensus in multi-agent systems with switching topologies and communication delays . Syst. Contr. Lett. , 2010 . 59 ( 6 ): 340 - 348 . DOI: 10.1016/j.sysconle.2010.03.009 http://doi.org/10.1016/j.sysconle.2010.03.009 .

H. Zhang , J. Chen . Bipartite consensus of linear muli-agent systems over signed digraphs: an output feedback control approach . Proc. 19th IFAC World Congress , 2014 . p.4681 - 4686 . DOI: 10.3182/20140824-6-ZA-1003.00608 http://doi.org/10.3182/20140824-6-ZA-1003.00608 .

H. Zhang , Z. Chen . Consensus acceleration in a class of predictive networks . IEEE Trans. Neur. Netw. Learn. Syst. , 2014 . 25 ( 10 ): 1921 - 1927 . DOI: 10.1109/TNNLS.2013.2294674 http://doi.org/10.1109/TNNLS.2013.2294674 .

H. Zhang , C. Zhai , Z. Chen . A general alignment repulsion algorithm for flocking of multi-agent systems . IEEE Trans. Automat. Contr. , 2011 . 56 ( 2 ): 430 - 435 . DOI: 10.1109/TAC.2010.2089652 http://doi.org/10.1109/TAC.2010.2089652 .

J. Zhong , Z. Lin , Z. Chen , 等 . Cooperative localization using angle-of-arrival information . Proc. 11th IEEE Int. Conf. on Control and Automation , 2014 . p.19 - 24 . DOI: 10.1109/ICCA.2014.6870889 http://doi.org/10.1109/ICCA.2014.6870889 .

G. Zhu , J. Hu . A distributed continuous-time algorithm for network localization using angle-of-arrival information . Automatica , 2014 . 50 ( 1 ): 53 - 63 . DOI: 10.1016/j.automatica.2013.09.033 http://doi.org/10.1016/j.automatica.2013.09.033 .

W. Zhu , D. Cheng . Leader-following consensus of second-order agents with multiple time-varying delays . Automatica , 2010 . 46 ( 12 ): 1994 - 1999 . DOI: 10.1016/j.automatica.2010.08.003 http://doi.org/10.1016/j.automatica.2010.08.003 .

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