AWB+CW TD=E$ AWB+CW^TD=E$的动量加速度梯度下降法，其最小Frobenius范数解及其在时变线性系统中的应用

IF 2.2 4区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

IET Control Theory and Applications Pub Date : 2025-07-11 DOI:10.1049/cth2.70047

Akbar Shirilord, Mehdi Dehghan

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引用次数: 0

摘要

本文提出了求解矩阵方程a WB + CW T D = E$ AWB + CW^T D = E$的梯度下降法。此外,该方法用于求解min W∥A W B + C W T优化问题D−E∥2$ \min _{W} \Vert AWB + CW^T D - E\Vert ^2$与Frobenius范数。我们对这些技术的收敛性和特点进行了全面的分析。为了提高收敛速度，我们引入了动量法的一种特殊变体。为了验证我们提出的迭代方法的有效性，我们提供了各种数值实例，并将结果与现有算法的结果进行了比较。最后，我们研究了在时变线性系统中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Gradient Descent Method With Momentum Acceleration for

A
W
B
+
C

W
T

D
=
E

$ AWB+CW^TD=E$
, Its Minimum Frobenius Norm Solution and Application in Time-Varying Linear Systems

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Gradient Descent Method With Momentum Acceleration for A W B + C W T D = E $ AWB+CW^TD=E$ , Its Minimum Frobenius Norm Solution and Application in Time-Varying Linear Systems

This study presents a gradient descent approach for addressing the matrix equation $A W B + C W^{T} D = E$ . Additionally, this method is utilized to solve the optimization problem $\min_{W} {∥ A W B + C W^{T} D - E ∥}^{2}$ with the Frobenius norm. We provide a comprehensive analysis of the convergence and characteristics of these techniques. To improve the convergence rate, we incorporate a specific variant of the momentum method. To validate the effectiveness of our proposed iterative methods, we offer various numerical examples and compare the outcomes with those of existing algorithms. Lastly, we investigate an application within the context of time-varying linear systems.

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来源期刊

IET Control Theory and Applications 工程技术-工程：电子与电气

CiteScore

5.70

自引率

7.70%

发文量

167

审稿时长

5.1 months

期刊介绍： IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces. Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed. Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.