Efficient Algorithm for the Computation of the Solution to a Sparse Matrix Equation in Distributed Control Theory

In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse equation at hand can be reduced to a system of linea...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 13; p. 1497
Main Authors: Pedroso, Leonardo, Batista, Pedro
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2021
Subjects:
Algorithms
Communication
Control theory
Decomposition
distributed control
distributed estimation
Dynamical systems
Floating point arithmetic
Linear equations
Sensors
Sparse matrices
sparse matrix
sparse matrix equation
Sparsity
sparsity constraint
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse equation at hand can be reduced to a system of linear equations. The proposed algorithm is shown to require significantly fewer floating point operations than the state-of-the-art solution. The proposed solution is applied to a real-life example, which models a wide range of industrial processes. The experimental results show that the solution put forward allows for a significant increase in efficiency in relation to the state-of-the-art solution. The significant increase in efficiency of the presented algorithm allows for a valuable widening of the applications of distributed estimation and control.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9131497