大系统模型简化的一种新的时域最优逼近法
A New Method of Optimal Time-Domain Approximation for Large-Scale System Model Reduction
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摘要: 从大系统及其降阶模型的单位脉冲响应矩阵近似相等出发,推导了大系统及其降阶模型 的特征值应该遵守的关系式.利用该关系式可以改进大系统模型简化的时域最优逼近法,将 泛函求极值的问题转化为参数优化的问题,有可能使问题的解决简单化.本文提出了两种算 法:1)保留主特征值的最优逼近;2)修改特征值的最优逼近.附有数字实例.Abstract: The relationship between the eigenvalues of both the large-scale system and its order-reduction model is derived from the requirement that their unit/impulse response matrices should be approximately equal to each other. With this formula, the time-domain optimal approximation for large-scale system simplification can be improved considerably, i.e. one needs only solve a parameter optimization problem instead of a functional problem. Two algorithms are proposed: 1, the optimal approximation with the dominant eigenvalues retained; 2, the optimal approximation with some eigenvalues modified. A numerical exam-pie is also attached.
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