Solving a system of linear equations: From centralized to distributed algorithms

P Wang, S Mou, J Lian, W Ren - Annual Reviews in Control, 2019 - Elsevier
For a wide range of control engineering applications, the problem of solving a system of
linear equations is often encountered and has been well studied. Traditionally, this problem …

A distributed algorithm for least squares solutions

X Wang, J Zhou, S Mou… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
In this technical note, a distributed algorithm is proposed for multiagent networks to achieve
a least squares solution of a system of linear equations, in which each agent only knows part …

Distributed least squares solver for network linear equations

T Yang, J George, J Qin, X Yi, J Wu - Automatica, 2020 - Elsevier
In this paper, we study the problem of finding the least square solutions of over-determined
linear algebraic equations over networks in a distributed manner. Each node has access to …

Distributed computation of linear matrix equations: An optimization perspective

X Zeng, S Liang, Y Hong, J Chen - IEEE Transactions on …, 2018 - ieeexplore.ieee.org
This paper investigates the distributed computation of the well-known linear matrix equation
in the form of AXB= F, with the matrices A, B, X, and F of appropriate dimensions, over …

Distributed algorithms of solving linear matrix equations via double-layered networks

Y Huang, X Zeng, Z Meng, D Meng - Automatica, 2024 - Elsevier
This paper focuses on designing distributed algorithms for solving the linear matrix equation
in the form of AXB= F via a double-layered multi-agent network. Firstly, we equivalently …

A distributed algorithm for solving linear algebraic equations over random networks

SS Alaviani, N Elia - IEEE Transactions on Automatic Control, 2020 - ieeexplore.ieee.org
This article considers the problem of solving linear algebraic equations of the form Ax= b
among multiagents, which seek a solution by using local information in presence of random …

Scalable distributed least square algorithms for large-scale linear equations via an optimization approach

Y Huang, Z Meng, J Sun - Automatica, 2022 - Elsevier
This paper proposes scalable distributed least square algorithms for solving large-scale
linear algebraic equations via multi-agent network. We consider two kinds of different …

Feedback of control on mathematics: Bettering iterative methods by observer system design

D Meng - IEEE Transactions on Automatic Control, 2022 - ieeexplore.ieee.org
The control approaches generally resort to the tools from the mathematics, but whether and
how the mathematics can benefit from the control approaches is unclear. This article aims to …

Continuous distributed algorithms for solving linear equations in finite time

X Shi, X Yu, J Cao, G Wen - Automatica, 2020 - Elsevier
This paper studies the distributed algorithms to obtain a solution of the linear equation A x=
b in finite time (FT) over a multi-agent network. In order to guarantee the settling time without …

Lyapunov criterion for stochastic systems and its applications in distributed computation

Y Qin, M Cao, BDO Anderson - IEEE Transactions on Automatic …, 2019 - ieeexplore.ieee.org
This paper presents new sufficient conditions for convergence and asymptotic or
exponential stability of a stochastic discrete-time system, under which the constructed …