k-Dimensional Agreement in Multiagent Systems

Given a network of agents, we study the problem of designing a distributed algorithm that computes <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> independent weighted means of the network's initial conditions (namely, the agents agree...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 69; no. 12; pp. 8978 - 8985
Main Authors: Bianchin, Gianluca, Vaquero, Miguel, Cortes, Jorge, Dall'Anese, Emiliano
Format: Journal Article
Language:English
Published: IEEE 01.12.2024
Subjects:
Computational modeling
Consensus algorithm
Consensus algorithms
decentralized control
graph theory
linear time-invariant (LTI) systems
Multi-agent systems
Protocols
Robot sensing systems
Sensors
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Given a network of agents, we study the problem of designing a distributed algorithm that computes <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> independent weighted means of the network's initial conditions (namely, the agents agree on a <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-dimensional space). Akin to average consensus, this problem finds applications in distributed computing and sensing, where agents seek to simultaneously evaluate <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> independent functions at a common point by running a single coordination algorithm. We show that linear algorithms can agree on quantities that are oblique projections of the vector of initial conditions, and we provide techniques to design protocols that are compatible with a pre-specified communication graph. More broadly, our results show that a single agreement algorithm can solve <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> consensus problems simultaneously at a fraction of the complexity of classical approaches but, in general, it requires higher network connectivity.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3431108