TY - GEN
T1 - Max Consensus in the Presence of Additive Noise
AU - Muniraju, Gowtham
AU - Tepedelenlioglu, Cihan
AU - Spanias, Andreas
AU - Zhang, Sai
AU - Banavar, Mahesh K.
N1 - Funding Information:
The authors from Arizona State University are funded in part by the NSF award ECSS 1307982
Funding Information:
The authors from Arizona State University are funded in part by the NSF award ECSS 1307982, NSF CPS award 1646542 and the SenSIP Center, School of ECEE, Arizona State University.
Publisher Copyright:
© 2018 IEEE.
PY - 2019/2/19
Y1 - 2019/2/19
N2 - The analysis of a distributed consensus algorithm for estimating the maximum of the node initial state values in a network is considered in the presence of communication noise. Conventionally, the maximum is estimated by updating the node state value with the largest received measurements in every iteration at each node. However, due to additive channel noise, the estimate of the maximum at each node has a positive drift at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used to study this ergodic process, wherein, at each iteration, the state values are multiplied by a random matrix characterized by the noise distribution. The growth rate of the state values due to noise is studied by analyzing the Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is bounded by a constant which depends on the spectral radius of the network and the noise variance. Simulation results supporting the theory are also presented.
AB - The analysis of a distributed consensus algorithm for estimating the maximum of the node initial state values in a network is considered in the presence of communication noise. Conventionally, the maximum is estimated by updating the node state value with the largest received measurements in every iteration at each node. However, due to additive channel noise, the estimate of the maximum at each node has a positive drift at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used to study this ergodic process, wherein, at each iteration, the state values are multiplied by a random matrix characterized by the noise distribution. The growth rate of the state values due to noise is studied by analyzing the Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is bounded by a constant which depends on the spectral radius of the network and the noise variance. Simulation results supporting the theory are also presented.
KW - Lyapunov exponent
KW - Max consensus
KW - max-plus algebra
KW - wireless sensor networks
UR - http://www.scopus.com/inward/record.url?scp=85062970075&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85062970075&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2018.8645297
DO - 10.1109/ACSSC.2018.8645297
M3 - Conference contribution
AN - SCOPUS:85062970075
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 1408
EP - 1412
BT - Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
Y2 - 28 October 2018 through 31 October 2018
ER -