CONTROLLABILITY OF NETWORK OPINION IN ERDOS-RENYI GRAPHS USING SPARSE CONTROL INPUTS

Geethu Joseph; Buddhika Nettasinghe; Vikram Krishnamurthy; Pramod K. Varshney

doi:10.1137/20M1327860

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CONTROLLABILITY OF NETWORK OPINION IN ERDOS-RENYI GRAPHS USING SPARSE CONTROL INPUTS

Journal article

Open access

Peer reviewed

CONTROLLABILITY OF NETWORK OPINION IN ERDOS-RENYI GRAPHS USING SPARSE CONTROL INPUTS

Geethu Joseph, Buddhika Nettasinghe, Vikram Krishnamurthy and Pramod K. Varshney

SIAM journal on control and optimization, Vol.59(3), pp.2321-2345

01/01/2021

DOI: 10.1137/20M1327860

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https://arxiv.org/pdf/2003.12817View

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Abstract

This paper considers a social network modeled as an Erdos-Renyi random graph. Each individual in the network updates her opinion using the weighted average of the opinions of her neighbors. We explore how an external manipulative agent can drive the opinions of these individuals to a desired state with a limited additive influence on their innate opinions. We show that the manipulative agent can steer the network opinion to any arbitrary value in finite time (i.e., the system is controllable) almost surely when there is no restriction on her influence. However, when the control input is sparsity constrained, the network opinion is controllable with some probability. We lower bound this probability using the concentration properties of random vectors based on the Levy concentration function and small ball probabilities. Our theoretical and numerical results shed light on how controllability of the network opinion depends on the parameters such as the size and the connectivity of the network and sity constraints faced by the manipulative agent.

Automation & Control Systems

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

Technology

Details

Title: Subtitle: CONTROLLABILITY OF NETWORK OPINION IN ERDOS-RENYI GRAPHS USING SPARSE CONTROL INPUTS
Creators: Geethu Joseph - Syracuse University
Buddhika Nettasinghe - Cornell University
Vikram Krishnamurthy - Cornell University
Pramod K. Varshney - Syracuse University
Resource Type: Journal article
Publication Details: SIAM journal on control and optimization, Vol.59(3), pp.2321-2345
DOI: 10.1137/20M1327860
ISSN: 0363-0129
eISSN: 1095-7138
Publisher: Siam Publications
Number of pages: 25
Grant note: ENG 60064237; 1714180 / National Science Foundation; National Science Foundation (NSF) W911NF-19-1-0365 / U.S. Army Research Office
Language: English
Date published: 01/01/2021
Academic Unit: Business Analytics
Record Identifier: 9984422735502771

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