通过 BCR 迭代法求解周期耦合算子矩阵方程及其在周期性状态反馈极点分配中的应用

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Wenling Wang, Caiqin Song
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引用次数: 0

摘要

目的 本文旨在利用双共轭残差算法研究周期耦合算子矩阵方程的约束解。新算法可以求解很多约束解,包括哈密顿解和对称解等特例。本文最后将新算法应用于极点分配问题。设计/方法/途径当所研究的周期耦合算子矩阵方程具有一致性时,证明约束解可以收敛到精确解。实验证明,新算法可以在任意初始矩阵的情况下,通过有限的迭代步数获得方程的解,且不会产生舍入误差。此外,当周期耦合算子矩阵的方程不一致时,也可以通过选择任意初始矩阵计算出最小规范约束解。研究结果数值实例表明,与现有的一些算法相比,所提出的方法具有更高的收敛效率,因为每次迭代使用的数据更少,而且数据足以完成一次更新。它不仅收敛精度最好,而且迭代所需的运行时间最少,大大节省了内存空间。原创性/价值与之前的算法相比,本文算法的主要特点是可以将这些方程合成在一起,得到一个耦合算子矩阵方程。虽然本文方程包含多个子矩阵方程,但本文算法在每次迭代时只需使用本文方程中一个子矩阵方程的信息,因此可以针对该类方程研究不同(耦合)矩阵方程的不同约束解。然而,以往的文章需要分别迭代矩阵方程的特定约束解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solving the periodic coupled operator matrix equations via BCR iterative method and its application in periodic state feedback pole assignment

Purpose

The paper aims to study the constraint solutions of the periodic coupled operator matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of constraint solutions including Hamiltonian solutions and symmetric solutions, as special cases. At the end of this paper, the new algorithm is applied to the pole assignment problem.

Design/methodology/approach

When the studied periodic coupled operator matrix equations are consistent, it is proved that constraint solutions can converge to exact solutions. It is demonstrated that the solutions of the equations can be obtained by the new algorithm with any arbitrary initial matrices without rounding error in a finite number of iterative steps. In addition, the least norm-constrained solutions can also be calculated by selecting any initial matrices when the equations of the periodic coupled operator matrix are inconsistent.

Findings

Numerical examples show that compared with some existing algorithms, the proposed method has higher convergence efficiency because less data are used in each iteration and the data is sufficient to complete an update. It not only has the best convergence accuracy but also requires the least running time for iteration, which greatly saves memory space.

Originality/value

Compared with previous algorithms, the main feature of this algorithm is that it can synthesize these equations together to get a coupled operator matrix equation. Although the equation of this paper contains multiple submatrix equations, the algorithm in this paper only needs to use the information of one submatrix equation in the equation of this paper in each iteration so that different constraint solutions of different (coupled) matrix equations can be studied for this class of equations. However, previous articles need to iterate on a specific constraint solution of a matrix equation separately.

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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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