### Abstract

A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.

Original language | English (US) |
---|---|

Article number | 8859263 |

Pages (from-to) | 779-791 |

Number of pages | 13 |

Journal | IEEE Transactions on Signal and Information Processing over Networks |

Volume | 5 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2019 |

### Fingerprint

### Keywords

- Max consensus
- max-plus algebra
- spectral radius
- wireless sensor networks

### ASJC Scopus subject areas

- Signal Processing
- Information Systems
- Computer Networks and Communications

### Cite this

**Analysis and design of robust max consensus for wireless sensor networks.** / Muniraju, Gowtham; Tepedelenlioglu, Cihan; Spanias, Andreas.

Research output: Contribution to journal › Article

*IEEE Transactions on Signal and Information Processing over Networks*, vol. 5, no. 4, 8859263, pp. 779-791. https://doi.org/10.1109/TSIPN.2019.2945639

}

TY - JOUR

T1 - Analysis and design of robust max consensus for wireless sensor networks

AU - Muniraju, Gowtham

AU - Tepedelenlioglu, Cihan

AU - Spanias, Andreas

PY - 2019/12

Y1 - 2019/12

N2 - A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.

AB - A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.

KW - Max consensus

KW - max-plus algebra

KW - spectral radius

KW - wireless sensor networks

UR - http://www.scopus.com/inward/record.url?scp=85073152728&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073152728&partnerID=8YFLogxK

U2 - 10.1109/TSIPN.2019.2945639

DO - 10.1109/TSIPN.2019.2945639

M3 - Article

AN - SCOPUS:85073152728

VL - 5

SP - 779

EP - 791

JO - IEEE Transactions on Signal and Information Processing over Networks

JF - IEEE Transactions on Signal and Information Processing over Networks

SN - 2373-776X

IS - 4

M1 - 8859263

ER -