高阶模型最优简化的积分平方误差法的若干性质

大系统的模型最优简化的积分平方误差法,至今仅仅对输入函数为脉冲、幂函数和正弦函数时有效。本文首先指出,指数函数等一类函数输入时的高阶模型也能用积分平方误差法进行最优简化。其次证明,和原系统有相同输出意义的等价系统具有叠加性,从而把高阶模型的最优简化工作推广到相当广泛的范围。 正弦函数输入时高阶模型的最优简化模型是与角频率有关的。本文最后给出,当角频率有偏离时,其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。

THE OPTIMAL REDUCTION OF HIGHER-ORDER MODELS

For optimal model-reduction of large scale systems, up to now, the integral-square-error method has been developed for systems with impulse, power or sine function inputs only. In this paper the author proves the following: (1) The optimal reduction of higher-order models with exponential inputs is also realizable. (2) The identical systems with same outputs have superposition property. (3) If a parameter in the inputs of the original large scale system deviates, the corresponding reduced order model can be changed by using the asymptotic expansion of the input functions.