A probabilistic analysis of the average consensus algorithm with quantized communication

Abstract In the average consensus problem the states of a set of agents, linked according to a directed graph, have to be driven to their average. When the communication between neighbors is uniformly quantized, such a problem can not be exactly solved by a linear time-invariant algorithm. In this work, we propose a probabilistic estimate of the error from the agreement, in terms of the eigenvalues of the evolution matrix describing the algorithm.

[1]  Peter Lancaster,et al.  The theory of matrices , 1969 .

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

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

[4]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

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

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

[7]  Mathew D. Penrose,et al.  Random Geometric Graphs , 2003 .

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

[9]  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..

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

[11]  Robert Elsässer,et al.  Distributing Unit Size Workload Packages in Heterogeneous Networks , 2006, J. Graph Algorithms Appl..

[12]  R. Srikant,et al.  Quantized Consensus , 2006, 2006 IEEE International Symposium on Information Theory.

[13]  R. Carli,et al.  Average consensus on networks with transmission noise or quantization , 2007, 2007 European Control Conference (ECC).

[14]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[15]  Ruggero Carli,et al.  Efficient quantized techniques for consensus algorithms , 2007 .

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

[17]  Jean-Charles Delvenne,et al.  Optimal strategies in the average consensus problem , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  Ruggero Carli,et al.  Communication constraints in the average consensus problem , 2008, Autom..

[19]  Optimal strategies in the average consensus problem , 2009, Syst. Control. Lett..

[20]  Ruggero Carli,et al.  Average consensus on networks with quantized communication , 2009 .

[21]  F. Bullo,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in d dimensions , .