MISO的离散动力系统的最小二乘模型降阶方法  

Model Reduction of MISO Discrete Dynamical Systems via Least Squares

作　　者：安玉娥[1] 张东[2] 梁玉梅[1] 

机构地区：[1]上海金融学院统计与数学学院,上海201209 [2]上海理工大学理学院,上海200093

出　　处：《数学的实践与认识》2016年第8期154-160,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11501363)

摘　　要：利用最小二乘原理,提出一个基于SVD-Krylov的模型降阶方法,方法兼顾基于SVD模型降阶方法的理论性质和基于Krylov模型降阶方法的有效计算,使得到的降阶系统既能匹配原系统的前r阶模,又能够保持系统的稳定性.利用对称矩阵特征值的极小极大原理,给出了保持系统稳定性的一个新的证明方法,与已有的方法相比,提出的理论证明方法更为简洁.对于离散系统,方法除了能匹配原模型的前r个Markov参数,还可将其推广到任意点处模匹配.数值例子也证明了方法的有效性.Inspired by the principle of least squares,we propose an SVD-Krylov based model reduction method.The method aims to combine the theoretical features of the SVD based methods with the efficient numerical implementation of the Krylov-based methods.The reduced model can match the first r moments of the full order model and the approach can guarantee stability.Compared to the existed methods,this paper presents a new and more concise proof about preserving stability by using the Max-Min principle.For discrete time systems,the reduced model can match the first r Markov parameters of the full order model.The method is generalized for moment matching at arbitrary interpolation points.The numerical examples verify the effectiveness of the method.

关 键 词：模型降阶 稳定性 模匹配 Markov参数 

分 类 号：O175[理学—数学]