多输入多输出大规模动力系统模型简化的Frobenius范数最小二乘法  

Model reduction of multiple-input and multiple-output large-scale dynamical systems via Frobenius norm least squares

作　　者：顾传青[1] 黎瑶[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2012年第4期368-375,共8页Communication on Applied Mathematics and Computation

基　　金：上海市自然科学基金资助项目(10ZR1410900);上海市重点学科建设资助项目(S30104)

摘　　要：对多输入多输出大规模动力系统的模型简化提出了一种新的方法.它是一种投影方法,其投影依赖于奇异值分解(singular value decomposition,SVD)和Krylov子空间.该方法实际上等价于求解一个Frobenius范数最小二乘问题.通过该方法降阶后的模型能准确地匹配原模型的前r个模,剩余的高阶模以Frobenius范数最小二乘法的形式逼近原模型的模,其中,r是降阶系统的维数.还将该方法推广到任意插值点的模匹配,数值例子也证明了该方法的有效性.A new method of model reduction for multiple-input and multiple-output large-scale dynamical systems is put forward. It is a kind of projection method, whose projection depends on the singular value decomposition （SVD） and the Krylov subspace. The method is actually equivalent to a Frobenius norm least squares problem. The reduced order model can accurately match the first r Markov／linebreak parameters of the original model, and the remaining high order models approach to the original model by the Frobenius norm least squares form, where r is the order of the reduced system. The method is also generalized to arbitrary interpolation point pattern matching. Numerical examples demonstrate the effectiveness of the method.

关 键 词：模型简化 模匹配 多输入多输出 块Hankel阵 Frobenius范数最小二乘法 投影 

分 类 号：O231[理学—运筹学与控制论]