Consensus with ternary messages

We provide a protocol for real-valued average consensus by networks of agents which exchange only a single message from the ternary alphabet {-1, 0, 1} between neighbors at each step. Our protocol works on time-varying undirected graphs subject to a connectivity condition, has a worst-case convergence time which is polynomial in the number of agents and the initial values, and requires no global knowledge about the graph topologies on the part of each node to implement except for knowing an upper bound on the degrees of its neighbors.

[1]  Paolo Frasca,et al.  Continuous-time quantized consensus: Convergence of Krasovskii solutions , 2011, Syst. Control. Lett..

[2]  F. Bullo,et al.  Motion Coordination with Distributed Information , 2007 .

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

[4]  Kai Cai,et al.  Quantized Consensus and Averaging on Gossip Digraphs , 2011, IEEE Transactions on Automatic Control.

[5]  Ruggero Carli,et al.  Gossip consensus algorithms via quantized communication , 2009, Autom..

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

[7]  Kai Cai,et al.  Convergence time analysis of quantized gossip consensus on digraphs , 2011, Autom..

[8]  Lihua Xie,et al.  Distributed Consensus With Limited Communication Data Rate , 2011, IEEE Transactions on Automatic Control.

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

[10]  Dimos V. Dimarogonas,et al.  Consensus with quantized relative state measurements , 2013, Autom..

[11]  Lihua Xie,et al.  Distributed consensus for multi-agent systems with communication delays and limited data rate , 2010, WCICA 2010.

[12]  Alexandros G. Dimakis,et al.  Geographic Gossip: Efficient Averaging for Sensor Networks , 2007, IEEE Transactions on Signal Processing.

[13]  Luca Schenato,et al.  Average TimeSynch: A consensus-based protocol for clock synchronization in wireless sensor networks , 2011, Autom..

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

[15]  Ruggero Carli,et al.  Optimal Synchronization for Networks of Noisy Double Integrators , 2011, IEEE Transactions on Automatic Control.

[16]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[17]  Ruggero Carli,et al.  Quantized average consensus via dynamic coding/decoding schemes , 2010 .

[18]  Han-Lim Choi,et al.  Consensus-Based Decentralized Auctions for Robust Task Allocation , 2009, IEEE Transactions on Robotics.

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

[20]  John N. Tsitsiklis,et al.  On Distributed Averaging Algorithms and Quantization Effects , 2008, IEEE Trans. Autom. Control..

[21]  Javad Lavaei,et al.  Quantized Consensus by Means of Gossip Algorithm , 2012, IEEE Transactions on Automatic Control.

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

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

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

[25]  Sanjeev R. Kulkarni,et al.  An upper bound on the convergence time for quantized consensus , 2013, INFOCOM.

[26]  Lihua Xie,et al.  Distributed consensus for multi-agent systems with communication delays and limited data rate , 2010, 2010 8th World Congress on Intelligent Control and Automation.

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

[28]  Alexander Olshevsky.  Consensus with ternary messages , 2013, 52nd IEEE Conference on Decision and Control.

[29]  Francesco Bullo,et al.  Notes on averaging over acyclic digraphs and discrete coverage control , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[30]  Gerardo Lafferriere,et al.  Decentralized control of vehicle formations , 2005, Syst. Control. Lett..

[31]  Lihua Xie,et al.  Sampled-data based average consensus with logarithmic quantizers , 2012, Proceedings of the 31st Chinese Control Conference.

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

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

[34]  Qun Li,et al.  Global Clock Synchronization in Sensor Networks , 2006, IEEE Trans. Computers.

[35]  Francesco Bullo,et al.  Consensus networks over finite fields , 2013, Autom..

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