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基于交叉Gram矩阵低秩分解的非对称线性系统的模型降阶

王雯,王玥,王文慧,肖志华   

  1. 长江大学信息与数学学院, 荆州 434023
  • 出版日期:2018-04-25 发布日期:2021-06-25

王雯, 王玥, 王文慧, 肖志华. 基于交叉Gram矩阵低秩分解的非对称线性系统的模型降阶[J]. 系统科学与数学, 2021, 41(4): 926-938.

WANG Wen, WANG Yue, WANG Wenhui , XIAO Zhihua. Model Order Reduction Based on Low-Rank Decomposition of the Cross Gramian for Non-Symmetric Linear Systems[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 926-938.

Model Order Reduction Based on Low-Rank Decomposition of the Cross Gramian for Non-Symmetric Linear Systems

WANG Wen, WANG Yue, WANG Wenhui ,XIAO Zhihua   

  1. School of Information and Mathematics, Yangtze University, Jingzhou 434023
  • Online:2018-04-25 Published:2021-06-25
针对非对称线性系统, 提出了一种基于交叉~Gram~矩阵低秩分解的 模型降阶方法. 该方法首先对原系统及其对偶系统的脉冲响应在~Legendre~多项式 基底下进行展开, 然后利用~Legendre~多项式的正交性, 给出非对称线性系统 交叉~Gram~矩阵的近似低秩分解, 进而通过投影变换得到原始系统的近似平衡 系统, 接着在给定的精度条件下, 构造满足精度的降阶模型. 该方法计算灵活、 高效, 且具有一定的自适应性. 最后, 数值算例验证了算法的有效性.
For non-symmetric linear systems, a model order reduction based on low-rank decomposition of the cross Gramian is proposed. The proposed approach first expands the impulse responses of the original system and its dual system in the space spanned by Legendre polynomials, and then the low-rank factors of the cross Gramian are directly constructed from the expansion coefficients by the orthogonality. After that, an approximate balanced system of the original system is obtained by projection transformation. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate Hankel singular values under the given tolerance of the approximation error. The method is flexible, efficient and adaptive. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
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