Reduced-order identification methods: Hierarchical algorithm or variable elimination algorithm

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-11-26 DOI:10.1016/j.automatica.2024.111991

Jing Chen , Yawen Mao , Dongqing Wang , Min Gan , Quanmin Zhu , Feng Liu

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引用次数: 0

Abstract

Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations; (2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates; (3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm.

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降阶识别方法：层次算法或变量消除算法

大规模系统广泛存在于机器学习和大数据技术中，而降阶识别算法通常被应用于这些领域。对于大规模系统识别，传统的最小二乘算法涉及高阶矩阵求逆计算，而传统的梯度下降算法收敛速度较慢。本文提出的降阶算法与前人的研究相比具有以下优点：（1）通过对参数向量的顺序分割，可以将高阶矩阵的逆计算简化为低阶矩阵的逆计算；（2）与梯度下降算法相比，降阶算法具有更好的条件信息矩阵，因此收敛速度更快；（3）通过使用艾特肯加速方法可以提高其收敛速度，因此基于降阶的艾特肯算法至少具有二次收敛性，且对步长没有限制。本文还给出了降阶算法的特性。仿真结果证明了所提算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.