A distributed algorithm for average consensus on strongly connected weighted digraphs

In this work we propose a distributed algorithm to solve the discrete-time average consensus problem on strongly connected weighted digraphs (SCWDs). The key idea is to couple the computation of the average with the estimation of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix according to the protocol described in Qu et al. (2012). The major contribution is the removal of the requirement of the knowledge of the out-neighborhood of an agent, thus paving the way for a simple implementation based on a pure broadcast-based communication scheme.

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

[2]  M. Haeri,et al.  Average consensus in networks of dynamic multi-agents with switching topology: infinite matrix products. , 2012, ISA transactions.

[3]  Christoforos N. Hadjicostis,et al.  Average Consensus in the Presence of Delays in Directed Graph Topologies , 2014, IEEE Transactions on Automatic Control.

[4]  B. Touri.  Product of Random Stochastic Matrices and Distributed Averaging , 2012 .

[5]  John N. Tsitsiklis,et al.  Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems , 2011, IEEE Transactions on Automatic Control.

[6]  S. Shankar Sastry,et al.  Tracking and Coordination of Multiple Agents Using Sensor Networks: System Design, Algorithms and Experiments , 2007, Proceedings of the IEEE.

[7]  Carlos Sagüés,et al.  Chebyshev Polynomials in Distributed Consensus Applications , 2011, IEEE Transactions on Signal Processing.

[8]  Andrea Gasparri,et al.  A Networked Transferable Belief Model Approach for Distributed Data Aggregation , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Frank L. Lewis,et al.  Cooperative control with distributed gain adaptation and connectivity estimation for directed networks , 2014 .

[10]  Kai Cai,et al.  Average consensus on general strongly connected digraphs , 2012, Autom..

[11]  Thomas C. Henderson,et al.  Leveraging RSSI for Robotic Repair of Disconnected Wireless Sensor Networks , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

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

[13]  John N. Tsitsiklis,et al.  Convergence Speed in Distributed Consensus and Averaging , 2009, SIAM J. Control. Optim..

[14]  Christoforos N. Hadjicostis,et al.  Distributed strategies for average consensus in directed graphs , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Yin Chen,et al.  Corrective consensus: Converging to the exact average , 2010, 49th IEEE Conference on Decision and Control (CDC).

[16]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[17]  Christoforos N. Hadjicostis,et al.  Distributed Matrix Scaling and Application to Average Consensus in Directed Graphs , 2013, IEEE Transactions on Automatic Control.