Decentralised minimal-time dynamic consensus

This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis.

[1]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

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

[3]  John N. Tsitsiklis,et al.  A Lower Bound for Distributed Averaging Algorithms on the Line Graph , 2011, IEEE Transactions on Automatic Control.

[4]  Peng Yang,et al.  Stability and Convergence Properties of Dynamic Average Consensus Estimators , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[6]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[7]  J.M. Maciejowski,et al.  Collective behavior coordination with predictive mechanisms , 2008, IEEE Circuits and Systems Magazine.

[8]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[9]  Ling Shi,et al.  Decentralised final value theorem for discrete-time LTI systems with application to minimal-time distributed consensus , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  Yongqiang Wang,et al.  On influences of global and local cues on the rate of synchronization of oscillator networks , 2011, Autom..

[11]  Wei Ren.  Consensus Seeking in Multi-vehicle Systems with a Time-varying Reference State , 2007, 2007 American Control Conference.

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

[13]  John N. Tsitsiklis,et al.  Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications , 2009, SIAM J. Control. Optim..

[14]  Ling Shi,et al.  Decentralised minimal-time consensus , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Brian D. O. Anderson,et al.  Agreeing Asynchronously , 2008, IEEE Transactions on Automatic Control.

[16]  Sandip Roy,et al.  Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator , 2011, Complex Syst..

[17]  Sonia Martínez,et al.  Discrete-time dynamic average consensus , 2010, Autom..

[18]  J. Tsitsiklis,et al.  A lower bound for distributed averaging algorithms , 2010, 1003.5941.

[19]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[20]  Richard M. Murray,et al.  DYNAMIC CONSENSUS FOR MOBILE NETWORKS , 2005 .

[21]  Louis M. Pecora,et al.  Synchronization of oscillators in complex networks , 2008 .

[22]  Siegfried M. Rump,et al.  Structured Perturbations Part I: Normwise Distances , 2003, SIAM J. Matrix Anal. Appl..

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

[24]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

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

[27]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[28]  J. Partington.  An introduction to Hankel operators , 1988 .

[29]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[30]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[31]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[33]  Markus A. Hitz,et al.  On computing nearest singular hankel matrices , 2005, ISSAC.

[34]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[35]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[36]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[37]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..