Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

Jiang Yao-Lin; Xu Kang-Li

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Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

机译：riemannian歧管上的线性和双线性系统的频率有限减少模型

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摘要

In this article, we propose two new iterative algorithms to solve the frequency-limited Riemannian optimization model order reduction problems of linear and bilinear systems. Different from the existing Riemannian optimization methods, we design a new Riemannian conjugate gradient scheme based on the Riemannian geometry notions on a product manifold, and then generate a new search direction. Theoretical analysis shows that the resulting search direction is always descent with depending neither on the line search used, nor on the convexity of the cost function. The proposed algorithms are also suitable for generating reduced systems over a frequency interval in bandpass form. Finally, two numerical examples are simulated to demonstrate the efficiency of our algorithms.

机译：在本文中，我们提出了两个新的迭代算法来解决线性和双线性系统的频率限制的Riemannian优化模型顺序减少问题。与现有的riemannian优化方法不同，我们设计了一种基于产品歧管上的riemannian几何概念的新的riemannian共轭梯度方案，然后生成新的搜索方向。理论分析表明，由此产生的搜索方向始终是下降，根据所使用的线路搜索，也不是成本函数的凸起。所提出的算法也适用于在带通形式中通过频率间隔产生减少的系统。最后，模拟了两个数值例子以展示我们算法的效率。

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来源
《IEEE Transactions on Automatic Control》 |2021年第9期|3938-3951|共14页
作者
Jiang Yao-Lin; Xu Kang-Li;
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作者单位

Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China;

Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China;

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正文语种 eng
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关键词
Manifolds; Optimization; Nonlinear systems; Linear systems; Frequency control; Geometry; Time-frequency analysis; Finite frequency; frequency-limited controllability and observability Gramians; iterative algorithm; model order reduction (MOR); product manifold; Riemannian optimization;

机译：歧管;优化;非线性系统;频率控制;几何;时间频率分析;有限频率;有限频率;频率有限的可控性和可观察性葛兰素;迭代算法;模型顺序减少（MOR）;产品歧管;黎曼优化;

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专利

1. GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS [J] . Xiaobao ZHU 数学物理学报（英文版） . 2016,第002期
2. Time- and frequency-limited H_2-optimal model order reduction of bilinear control systems [J] . Zulfiqar Umair, Sreeram Victor, Ilyas Ahmad Mian, International journal of systems science . 2021,第9a12期

机译：时间和频率限制的H_2-最佳模型顺序减少双线性控制系统
3. Reduced-order models of 2-D linear discrete separable-denominator system using bilinear Routh approximations [J] . Tong-Yi Guo, Chyi Hwang IEE Proceedings. Part G, Circuits, Devices and Systems . 1992,第1期

机译：使用双线性Routh逼近的二维线性离散可分母系统的降阶模型
4. Reduction, Linearization, and Stability of Relative Equilibria for Mechanical Systems on Riemannian Manifolds [J] . Francesco Bullo, Andrew D. Lewis Acta Applicandae Mathematicae . 2007,第1期

机译：黎曼流形上机械系统的相对平衡的约化，线性化和稳定性
5. Multivariate General Linear Models (MGLM) on Riemannian Manifolds with Applications to Statistical Analysis of Diffusion Weighted Images [C] . Kim Hyunwoo J., Bendlin Barbara B., Adluru Nagesh, IEEE Conference on Computer Vision and Pattern Recognition . 2014

机译：利莫曼歧管的多变量通用线性模型（MGLM）与扩散加权图像统计分析的应用
6. Identification of discrete time bilinear systems through equivalent linear models. [D] . Hizir, Necdet Berk. 2010

机译：通过等效线性模型识别离散时间双线性系统。
7. Multivariate General Linear Models (MGLM) on Riemannian Manifolds with Applications to Statistical Analysis of Diffusion Weighted Images [O] . Hyunwoo J. Kim, Nagesh Adluru, Maxwell D. Collins, -1

机译：黎曼流形上的多元通用线性模型（MGLM）及其在扩散加权图像统计分析中的应用
8. Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds [O] . Francesco Bullo, Andrew D. Lewis 2013

机译：黎曼流形上机械系统的相对平衡的简化，线性化和稳定性
9. Physical lumping methods for developing linear reduced models for high speed propulsion systems [R] . Immel, S. M., Hartley, Tom T., Deabreu-Garcia, J. Alex 1991

机译：用于开发高速推进系统的线性简化模型的物理集总方法

Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

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