Higher dimensional consensus algorithms in sensor networks

This paper introduces higher dimensional consensus, a framework to capture a number of different, but, related distributed, iterative, linear algorithms of interest in sensor networks. We show that, by suitably choosing the iteration matrix of the higher dimensional consensus, we can capture, besides the standard average-consensus, a broad range of applications, including sensor localization, leader-follower, and distributed Jacobi algorithm. We work with the concept of anchors and explicitly derive the consensus subspace and provide the dimension of the limiting state of the sensors.

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

[2]  K. Khalil.  On the Complexity of Decentralized Decision Making and Detection Problems , 2022 .

[3]  V. S. Anil Kumar,et al.  Distributed Algorithms for Constructing Approximate Minimum Spanning Trees in Wireless Sensor Networks , 2009, IEEE Transactions on Parallel and Distributed Systems.

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

[5]  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.

[6]  José M. F. Moura,et al.  Distributing the Kalman Filter for Large-Scale Systems , 2007, IEEE Transactions on Signal Processing.

[7]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

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

[9]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures , 2007, IEEE Transactions on Signal Processing.

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

[11]  M. Mesbahi,et al.  Pulling the Strings on Agreement: Anchoring, Controllability, and Graph Automorphisms , 2007, 2007 American Control Conference.

[12]  Soummya Kar,et al.  Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes , 2008, IEEE Transactions on Signal Processing.

[13]  G. Shilov,et al.  Linear Algebra , 1971 .