Open AccessDistributed optimisation approach to least‐squares solution of Sylvester equations
Author(s) -
Deng Wen,
Zeng Xianlin,
Hong Yiguang
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.1400
Subject(s) - sylvester equation , equivalence (formal languages) , convergence (economics) , partition (number theory) , mathematical optimization , least squares function approximation , mathematics , regular polygon , row , computer science , stability (learning theory) , algorithm , eigenvalues and eigenvectors , discrete mathematics , combinatorics , physics , statistics , geometry , quantum mechanics , estimator , database , machine learning , economics , economic growth
In this study, the authors design distributed algorithms for solving the Sylvester equation A X + X B = C in the sense of least squares over a multi‐agent network. In the problem setup, every agent in the interconnected system only has local information of some columns or rows of data matrices A, B and C , and exchanges information among neighbour agents. They propose algorithms with mainly focusing on a specific partition case, whose designs can be easily generalised to other partitions. Three distributed continuous‐time algorithms aim at two cases for seeking a least‐squares/regularisation solution from the viewpoint of optimisation. Due to the equivalence between an equilibrium point of each system under discussion and an optimal solution to the corresponding optimisation problem, the authors make use of semi‐stability theory and methods in convex optimisation to prove convergence theorems of proposed algorithms that arrive at a least‐squares/regularisation solution.