缺阶有理密度的谱因式分解

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-02-20 DOI:10.1137/23m1546622

Wenqi Cao, Anders Lindquist

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 1 期第 776-798 页，2024 年 2 月。摘要尽管有数百篇关于有理谱因式分解的论文，但其中大多数涉及全秩谱密度。在本文中，我们提出了一种新的秩缺谱密度谱因式分解方法，从而在离散时间和连续时间两种情况下得到最小相全秩谱因式。与几种低秩谱因式分解方法相比，我们的方法利用了因式内部的确定性关系，从而提高了计算效率。此外，我们还证明了这种方法很容易用于低阶过程的识别和维纳滤波。

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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Spectral Factorization of Rank-Deficient Rational Densities

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 776-798, February 2024.
Abstract. Though there are hundreds of papers on rational spectral factorization, most of them are concerned with full-rank spectral densities. In this paper we propose a novel approach for spectral factorization of a rank-deficient spectral density, leading to a minimum-phase full-rank spectral factor, in both the discrete-time and continuous-time cases. Compared with several approaches to low-rank spectral factorization, our approach exploits a deterministic relation inside the factor, leading to high computational efficiency. In addition, we show that this method is easily used in identification of low-rank processes and in Wiener filtering.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.