Distributed Predefined-Time Algorithm for System of Linear Equations Over Directed Networks

In this brief, we propose a predefined-time algorithm based on multi-agent networks for solving linear equations of the form <inline-formula> <tex-math notation="LaTeX">Ax = b </tex-math></inline-formula>, where the predefined-time can be predesigned by the user and...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Vol. 71; no. 4; pp. 2139 - 2143
Main Authors: Lian, Mengke, Guo, Zhenyuan, Wen, Shiping, Huang, Tingwen
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Convergence
Directed graphs
Distributed algorithm
Distributed algorithms
Formulas (mathematics)
Graph theory
Linear equations
Mathematical analysis
multi-agent network
Multi-agent systems
Multiagent systems
Optimization
predefined-time
Signal processing algorithms
Symmetric matrices
system of linear equations
ISSN:1549-7747, 1558-3791
Online Access:Get full text
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Summary:In this brief, we propose a predefined-time algorithm based on multi-agent networks for solving linear equations of the form <inline-formula> <tex-math notation="LaTeX">Ax = b </tex-math></inline-formula>, where the predefined-time can be predesigned by the user and each agent only knows partial rows of the augmented matrix <inline-formula> <tex-math notation="LaTeX">(A\; b) </tex-math></inline-formula>. By reformulating the system of linear equations as an unconstrained optimization problem and applying the time-base generator technology to optimization approaches, we provide a gradient-based predefined-time algorithm over weight-balanced directed graphs, which can converge to a solution at a given time. Finally, this theoretical results are illustrated by a numerical examples.
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ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2023.3333325