中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (2): 1-5.

• 研究论文 •    下一篇

求解大规模线性时不变系统的最优H2模型降阶问题的共轭梯度法

曾泰山1,鲁春元2,陈 剑3   

  1. (1中山大学数学与计算科学学院,广东 广州 510275;2广东药学院医药信息工程学院,广东 广州510006;3佛山科学技术学院数学系,广东 佛山528000)
  • 收稿日期:2010-04-30 修回日期:1900-01-01 出版日期:2011-03-25 发布日期:2011-03-25

A Conjugated Gradient Algorithm for Optimal H2 Model Reduction of Large Scale Dynamical Systems

ZENG Taishan1,LU Chunyuan2,CHEN Jian3   

  1. (1School of Mathematics and Computational Science, Sun Yatsen University, Guangzhou 510275, China;2College of Medical Information Engineering, Guangdong Pharmaceutical University, Guangzhou 510006,China;3Department of Mathematics, Foshan University, Foshan 528000,China)
  • Received:2010-04-30 Revised:1900-01-01 Online:2011-03-25 Published:2011-03-25

摘要: 针对最优H2模型降阶问题,提出了适合大规模多输入多输出系统的共轭梯度法。该方法仅需利用一阶导数信息,存储量少,计算复杂度低,且具有超线性收敛性。实验结果显示了算法的有效性。

关键词: 模型降阶, 共轭梯度法, Grassmann流形, 线性时+不变系统

Abstract:

A conjugated gradient algorithm with superlinear convergence which is suitable for the optimal H2 model reduction of the multiinput multi-output large scale dynamical systems is proposed. The proposed algorithm computes only first-order derivative of the cost function. It has low storage requirement and computational cost. Numerical example demonstrates the approximation accuracy and computational efficiency.

Key words: model reduction, conjugated gradient method, Grassmann manifold, linear time invariant system

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