Analysis of consensus protocols with bounded measurement errors

This paper analyzes two classes of consensus algorithms in the presence of bounded measurement errors. The considered protocols adopt an updating rule based either on constant or vanishing weights. Under the assumption of bounded error, the consensus problem is cast in a set-membership framework, and the agreement of the team is studied by analyzing the evolution of the feasible state set. Bounds on the asymptotic difference between the states of the agents are explicitly derived, in terms of the bounds on the measurement noise and the values of the weight matrix.

[1]  Minghui Zhu,et al.  Dynamic average consensus on synchronous communication networks , 2008, 2008 American Control Conference.

[2]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[3]  Andrea Garulli,et al.  A set-membership approach to consensus problems with bounded measurement errors , 2008, 2008 47th IEEE Conference on Decision and Control.

[4]  Antonio Vicino,et al.  Optimal estimation theory for dynamic systems with set membership uncertainty: An overview , 1991, Autom..

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

[6]  Wei Ren,et al.  Consensus algorithms are input-to-state stable , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[8]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[9]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[10]  Laura Giarré,et al.  Consensus for Networks with Unknown but Bounded Disturbances , 2009, SIAM J. Control. Optim..

[11]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[12]  Randy A. Freeman,et al.  Decentralized Environmental Modeling by Mobile Sensor Networks , 2008, IEEE Transactions on Robotics.

[13]  Emilio Frazzoli,et al.  On synchronous robotic networks Part II: Time complexity of rendezvous and deployment algorithms , 2007, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Luigi Chisci,et al.  Recursive state bounding by parallelotopes , 1996, Autom..

[15]  Jonathan H. Manton,et al.  Stochastic approximation for consensus seeking: Mean square and almost sure convergence , 2007, 2007 46th IEEE Conference on Decision and Control.

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

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

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

[19]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

[21]  Milos Zefran,et al.  Rendezvous under noisy measurements , 2008, 2008 47th IEEE Conference on Decision and Control.