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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Veröffentlicht in:IEEE transactions on circuits and systems. II, Express briefs Jg. 71; H. 4; S. 2139 - 2143
Hauptverfasser: Lian, Mengke, Guo, Zhenyuan, Wen, Shiping, Huang, Tingwen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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
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Abstract 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.
AbstractList In this brief, we propose a predefined-time algorithm based on multi-agent networks for solving linear equations of the form [Formula Omitted], where the predefined-time can be predesigned by the user and each agent only knows partial rows of the augmented matrix [Formula Omitted]. 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.
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.
Author Lian, Mengke
Wen, Shiping
Huang, Tingwen
Guo, Zhenyuan
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In this brief, we propose a predefined-time algorithm based on multi-agent networks for solving linear equations of the form [Formula Omitted], where the...
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SubjectTerms 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
Title Distributed Predefined-Time Algorithm for System of Linear Equations Over Directed Networks
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