单输入单输出大规模动力系统模型的简化方法

Model reduction for SISO large-scale dynamical systems

提出的简化单输入单输出大规模动力系统的一种新方法是系统在等式约束最小二乘法的一种推广.这种方法是一种投影方法,其投影依赖于奇异分解和Krylov子空间.通过平移算子,使得降阶模型与原模型的前r+i模准确地匹配,剩余的高阶模利用拉格朗日乘子法进行等式约束最小二乘的形式逼近原模.通过拉格朗日乘子法来求解具有约束条件的最小二乘问题,让推导出来的用于模型简化的投影变换矩阵更为简便.

We use a generalization of equality constrained least squares method for single input singel output （SISO） systems to reduce model for SISO large-scale dynamical systems. This method is a two-sided projection method where one side reflects the single value decomposition（SVD） part and the other side reflects the block Krylov part. We use the shift operator to match the first r ＋ i Markov parameters of the full order model, and the remaining ones approximation in a Lagrange least squares sense without being explicitly computed. The projective matrix for model reduction is more simple.