Consensus Theory in Networked Systems

This chapter provides a theoretical analysis for consensus reaching in networked systems. Convergence analysis is carried out for distributed algorithms on directed weighted networks for continuous- and discrete-time cases. Also, systems where consensus can not be reached from every initial state have been studied. We describe the connections between spectral and structural properties of complex networks and the convergence rate of consensus algorithms. Theoretical results regarding consensus-seeking under dynamically changing communication topologies and communication time delays are summarized. Consensus algorithms for double-integrator dynamics are described in the context of cooperative control of multivehicle systems.

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

[2]  Soummya Kar,et al.  Gossip Algorithms for Distributed Signal Processing , 2010, Proceedings of the IEEE.

[3]  Dimos V. Dimarogonas,et al.  On the Rendezvous Problem for Multiple Nonholonomic Agents , 2007, IEEE Transactions on Automatic Control.

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

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

[6]  Manfredi Maggiore,et al.  State Agreement for Continuous-Time Coupled Nonlinear Systems , 2007, SIAM J. Control. Optim..

[7]  Kevin M. Passino,et al.  Stability analysis of swarms , 2003, IEEE Trans. Autom. Control..

[8]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[9]  H.G. Tanner,et al.  State synchronization in local-interaction networks is robust with respect to time delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[11]  P. Chebotarev,et al.  Forest Matrices Around the Laplaeian Matrix , 2002, math/0508178.

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

[13]  Stephen P. Boyd.  Convex optimization of graph Laplacian eigenvalues , 2006 .

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

[15]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[16]  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.

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

[18]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[19]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. Part 2: The Asynchronous Case , 2007, SIAM J. Control. Optim..

[20]  Panos J. Antsaklis,et al.  Networked Embedded Sensing and Control , 2006 .

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

[22]  Nancy A. Lynch,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

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

[24]  P. Chebotarev,et al.  On of the Spectra of Nonsymmetric Laplacian Matrices , 2004, math/0508176.

[25]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

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

[27]  R.W. Beard,et al.  Multi-agent Kalman consensus with relative uncertainty , 2005, Proceedings of the 2005, American Control Conference, 2005..

[28]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

[29]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

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

[31]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[32]  Wei Ren,et al.  Consensus strategies for cooperative control of vehicle formations , 2007 .

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

[34]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[37]  Pavel Yu. Chebotarev,et al.  Coordination in multiagent systems and Laplacian spectra of digraphs , 2009, ArXiv.

[38]  Wei Ren,et al.  Distributed attitude alignment in spacecraft formation flying , 2007 .

[39]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[40]  Wenwu Yu,et al.  Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[42]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

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

[44]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks , 2011 .