Consensus and Cooperation in Networked Multi-Agent Systems

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

[1]  J. Wolfowitz.  Products of indecomposable, aperiodic, stochastic matrices , 1963 .

[2]  M. Murty.  Ramanujan Graphs , 1965 .

[3]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[4]  M. Degroot.  Reaching a Consensus , 1974 .

[5]  John N. Tsitsiklis,et al.  Convergence and asymptotic agreement in distributed decision problems , 1982 .

[6]  V. Borkar,et al.  Asymptotic agreement in distributed estimation , 1982 .

[7]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .

[8]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[9]  B. Bollobás.  The evolution of random graphs , 1984 .

[10]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[11]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[13]  John N. Tsitsiklis,et al.  Distributed asynchronous deterministic and stochastic gradient optimization algorithms , 1986 .

[14]  George Cybenko,et al.  Dynamic Load Balancing for Distributed Memory Multiprocessors , 1989, J. Parallel Distributed Comput..

[15]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[16]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[17]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[18]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[19]  Jon Atli Benediktsson,et al.  Consensus theoretic classification methods , 1992, IEEE Trans. Syst. Man Cybern..

[20]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[21]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[22]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[23]  D. Spielman,et al.  Expander codes , 1996 .

[24]  S C Weller,et al.  Assessing Rater Performance without a "Gold Standard" Using Consensus Theory , 1997, Medical decision making : an international journal of the Society for Medical Decision Making.

[25]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[26]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[27]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[28]  Kristi A. Morgansen,et al.  Limited communication control , 1999 .

[29]  Masafumi Yamashita,et al.  Distributed memoryless point convergence algorithm for mobile robots with limited visibility , 1999, IEEE Trans. Robotics Autom..

[30]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[31]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[32]  Chris Hanson,et al.  Amorphous computing , 2000, Commun. ACM.

[33]  M. Egerstedt,et al.  Formation constrained multi-agent control , 2001, IEEE Trans. Robotics Autom..

[34]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[35]  A. Rbnyi.  ON THE EVOLUTION OF RANDOM GRAPHS , 2001 .

[36]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[37]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[38]  Radhika Nagpal,et al.  Programmable self-assembly using biologically-inspired multiagent control , 2002, AAMAS '02.

[39]  F. Bullo,et al.  Coverage control for mobile sensing networks , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[40]  Eric Klavins,et al.  Communication Complexity of Multi-robot Systems , 2002, WAFR.

[41]  Peter N. Belhumeur,et al.  Closing ranks in vehicle formations based on rigidity , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[42]  J. A. Fax.  Optimal and Cooperative Control of Vehicle Formations , 2002 .

[43]  Richard M. Murray,et al.  DISTRIBUTED COOPERATIVE CONTROL OF MULTIPLE VEHICLE FORMATIONS USING STRUCTURAL POTENTIAL FUNCTIONS , 2002 .

[44]  R. Murray,et al.  Graph rigidity and distributed formation stabilization of multi-vehicle systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[45]  William B. Dunbar,et al.  Cooperative control of multi-vehicle systems using cost graphs and optimization , 2003, Proceedings of the 2003 American Control Conference, 2003..

[46]  Richard M. Murray,et al.  Flocking with obstacle avoidance: cooperation with limited communication in mobile networks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[47]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[48]  Jie Lin,et al.  The multi-agent rendezvous problem , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[49]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[50]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

[51]  C.J. Tomlin,et al.  Decentralized spacing control of a string of multiple vehicles over lossy datalinks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[52]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[53]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[54]  B. Anderson,et al.  Sensor and network topologies of formations with direction, bearing, and angle information between agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[55]  Mehran Mesbahi,et al.  On state-dependent dynamic graphs and their controllability properties , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[56]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[57]  Vijay Kumar,et al.  Leader-to-formation stability , 2004, IEEE Transactions on Robotics and Automation.

[58]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[59]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[60]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[61]  Magnus Egerstedt,et al.  Connectivity graphs as models of local interactions , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[62]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[63]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[64]  Mehran Mesbahi,et al.  Agreement over random networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[65]  A. Jadbabaie,et al.  On the stability of the Kuramoto model of coupled nonlinear oscillators , 2005, Proceedings of the 2004 American Control Conference.

[66]  F. Borrelli,et al.  A study on decentralized receding horizon control for decoupled systems , 2004, Proceedings of the 2004 American Control Conference.

[67]  Andrey V. Savkin,et al.  Coordinated collective motion of Groups of autonomous mobile robots: analysis of Vicsek's model , 2004, IEEE Transactions on Automatic Control.

[68]  Emilio Frazzoli,et al.  On synchronous robotic networks Part I: Models, tasks and complexity notions , 2007, Proceedings of the 44th IEEE Conference on Decision and Control.

[69]  P.J. Antsaklis,et al.  Asynchronous Consensus Protocols: Preliminary Results, Simulations and Open Questions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[70]  K.J. Kyriakopoulos,et al.  Formation Control and Collision Avoidance for Multi-Agent Systems and a Connection between Formation Infeasibility and Flocking Behavior , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[71]  G. Verghese,et al.  Synchronization in Generalized Erdös-Rényi Networks of Nonlinear Oscillators , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[72]  M. Spong,et al.  On Synchronization of Kuramoto Oscillators , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[73]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[74]  E.H. Abed,et al.  Formation Control with Virtual Leaders and Reduced Communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[75]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[76]  M. Cao,et al.  A Lower Bound on Convergence of a Distributed Network Consensus Algorithm , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[77]  A. Jadbabaie,et al.  Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[78]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[79]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[80]  M. Alighanbari,et al.  Decentralized Task Assignment for Unmanned Aerial Vehicles , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[81]  Jeff S. Shamma,et al.  Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria , 2005, IEEE Transactions on Automatic Control.

[82]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[83]  Venkatesh Saligrama Murat Alanyali Onur Savas.  Asynchronous Distributed Detection in Sensor Networks ∗ , 2005 .

[84]  George J. Pappas,et al.  Controlling Connectivity of Dynamic Graphs , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[85]  R.M. Murray,et al.  On Sensor Fusion in the Presence of Packet-dropping Communication Channels , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[86]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[87]  Richard M. Murray,et al.  DYNAMIC CONSENSUS FOR MOBILE NETWORKS , 2005 .

[88]  J. Cortés.  Achieving coordination tasks in finite time via nonsmooth gradient flows , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[89]  A. Jadbabaie,et al.  Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[90]  R. Pesenti,et al.  Distributed Consensus in Networks of Dynamic Agents , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[91]  Xiaobo Tan,et al.  A Stochastic Algorithm for Self-Organization of Autonomous Swarms , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[92]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[93]  Emilio Frazzoli,et al.  On synchronous robotic networks Part II: Time complexity of rendezvous and deployment algorithms , 2007, Proceedings of the 44th IEEE Conference on Decision and Control.

[94]  Stephen P. Boyd,et al.  Gossip algorithms: design, analysis and applications , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[95]  Richard M. Murray,et al.  Approximate distributed Kalman filtering in sensor networks with quantifiable performance , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[96]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[97]  Naomi Ehrich Leonard,et al.  Collective motion and oscillator synchronization , 2005 .

[98]  M. Mesbahi,et al.  Relative Sensing Networks: Observability, Estimation, and the Control Structure , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[99]  Dongyan Xu,et al.  Robust computation of aggregates in wireless sensor networks: distributed randomized algorithms and analysis , 2005 .

[100]  C. Tomlin,et al.  Interesting conjugate points in formation constrained optimal multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[101]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[102]  R.M. Murray,et al.  Distributed Averaging on Asynchronous Communication Networks , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[103]  Meng Ji,et al.  Connectedness preserving distributed coordination control over dynamic graphs , 2005, Proceedings of the 2005, American Control Conference, 2005..

[104]  G. Verghese,et al.  Synchronization in Generalized Erdös-Rényi Networks of Nonlinear Oscillators , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[105]  Laura Giarré,et al.  Non-linear protocols for optimal distributed consensus in networks of dynamic agents , 2006, Syst. Control. Lett..

[106]  Peng Yang,et al.  Distributed estimation and control of swarm formation statistics , 2006, 2006 American Control Conference.

[107]  M. Alanyali,et al.  Distributed Detection in Sensor Networks With Packet Losses and Finite Capacity Links , 2006, IEEE Transactions on Signal Processing.

[108]  R. Olfati-Saber,et al.  Swarms on Sphere: A Programmable Swarm with Synchronous Behaviors like Oscillator Networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[109]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[110]  Namir,et al.  Authors , 1947, Praxis der Kinderpsychologie und Kinderpsychiatrie.

[111]  J. Shamma,et al.  Belief consensus and distributed hypothesis testing in sensor networks , 2006 .

[112]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[113]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[114]  F. Bullo,et al.  On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms , 2007, IEEE Transactions on Automatic Control.

[115]  F. Bullo,et al.  On Synchronous Robotic Networks—Part I: Models, Tasks, and Complexity , 2005, IEEE Transactions on Automatic Control.

[116]  Ali Jadbabaie,et al.  Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents , 2007, IEEE Transactions on Automatic Control.

[117]  R. O. Saber.  Consensus and cooperation in networked multi-Agent systems , 2007 .

[118]  M. Johansson,et al.  Faster Linear Iterations for Distributed Averaging , 2008 .

[119]  L. Asz.  Random Walks on Graphs: a Survey , 2022 .