Finite-time distributed averaging

This paper proposes a distributed averaging algorithm for multi-agent networks, in which each agent is with a real-valued measurement. Provided that the underlying graph of the network is a tree, the proposed algorithm enables each agent to compute the average of the values of all agents in the network in a finite number of steps. Different from most existing finite-time distributed averaging algorithms, the algorithm proposed in this paper does not require each agent to know any global information.

[1]  Shaoshuai Mou,et al.  Deterministic gossiping with a periodic protocol , 2010, 49th IEEE Conference on Decision and Control (CDC).

[2]  Brian D. O. Anderson,et al.  Local average consensus in distributed measurement of spatial-temporal varying parameters: 1D case , 2013, CDC.

[3]  Ling Shi,et al.  Decentralised minimum-time consensus , 2013, Autom..

[4]  Shaoshuai Mou,et al.  Towards optimal convex combination rules for gossiping , 2013, 2013 American Control Conference.

[5]  Shaoshuai Mou,et al.  A distributed algorithm for solving a linear algebraic equation , 2015, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

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

[8]  Shaoshuai Mou,et al.  Distributed Averaging Using Compensation , 2013, IEEE Communications Letters.

[9]  Wei Ren On Consensus Algorithms for Double-Integrator Dynamics , 2008, IEEE Trans. Autom. Control..

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

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

[12]  John N. Tsitsiklis,et al.  Weighted Gossip: Distributed Averaging using non-doubly stochastic matrices , 2010, 2010 IEEE International Symposium on Information Theory.

[13]  Shaoshuai Mou,et al.  Deterministic Gossiping , 2011, Proceedings of the IEEE.

[14]  Baruch Awerbuch,et al.  Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems , 1987, STOC.

[15]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[16]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[17]  C.N. Hadjicostis,et al.  Finite-Time Distributed Consensus in Graphs with Time-Invariant Topologies , 2007, 2007 American Control Conference.

[18]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[19]  Alain Y. Kibangou,et al.  Graph Laplacian based matrix design for finite-time distributed average consensus , 2012, 2012 American Control Conference (ACC).

[20]  Christian Lavault,et al.  A distributed algorithm for constructing a minimum diameter spanning tree , 2004, J. Parallel Distributed Comput..

[21]  Fenghua He,et al.  Periodic Gossiping , 2011 .

[22]  Alain Y. Kibangou Finite-time average consensus based protocol for distributed estimation over AWGN channels , 2011, IEEE Conference on Decision and Control and European Control Conference.

[23]  Alain Y. Kibangou,et al.  Consensus-based distributed estimation of Laplacian eigenvalues of undirected graphs , 2013, 2013 European Control Conference (ECC).

[24]  Refael Hassin,et al.  Minimum Restricted Diameter Spanning Trees , 2002, APPROX.

[25]  Pierre A. Humblet,et al.  A Distributed Algorithm for Minimum-Weight Spanning Trees , 1983, TOPL.

[26]  R.W. Beard,et al.  Discrete-time average-consensus under switching network topologies , 2006, 2006 American Control Conference.

[27]  Shaoshuai Mou,et al.  A fixed-neighbor, distributed algorithm for solving a linear algebraic equation , 2013, 2013 European Control Conference (ECC).

[28]  Shaoshuai Mou,et al.  Request-based gossiping , 2011, IEEE Conference on Decision and Control and European Control Conference.

[29]  Shreyas Sundaram,et al.  Distributed function calculation and consensus using linear iterative strategies , 2008, IEEE Journal on Selected Areas in Communications.

[30]  Xiaojie Gao,et al.  On matrix factorization and finite-time average-consensus , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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