### Abstract

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.

Original language | English (US) |
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Title of host publication | Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 |

Editors | Michael B. Matthews |

Publisher | IEEE Computer Society |

Pages | 1408-1412 |

Number of pages | 5 |

ISBN (Electronic) | 9781538692189 |

DOIs | |

State | Published - Feb 19 2019 |

Event | 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 - Pacific Grove, United States Duration: Oct 28 2018 → Oct 31 2018 |

### Publication series

Name | Conference Record - Asilomar Conference on Signals, Systems and Computers |
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Volume | 2018-October |

ISSN (Print) | 1058-6393 |

### Conference

Conference | 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 |
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Country | United States |

City | Pacific Grove |

Period | 10/28/18 → 10/31/18 |

### Fingerprint

### Keywords

- Lyapunov exponent
- Max consensus
- max-plus algebra
- wireless sensor networks

### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

### Cite this

*Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018*(pp. 1408-1412). [8645297] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2018.8645297

**Max Consensus in the Presence of Additive Noise.** / Muniraju, Gowtham; Tepedelenlioglu, Cihan; Spanias, Andreas; Zhang, Sai; Banavar, Mahesh K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018.*, 8645297, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2018-October, IEEE Computer Society, pp. 1408-1412, 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018, Pacific Grove, United States, 10/28/18. https://doi.org/10.1109/ACSSC.2018.8645297

}

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.

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

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

ER -