We propose an adaptive moment-matching framework for model order reduction of quadratic-bilinear systems. In this framework, an important issue is the selection of those shift frequencies where moment-matching is to be achieved. So far, the choice often has been random or linked to the linear part of the nonlinear system. In this paper, we extend the use of an existing a posteriori error bound for general linear time invariant systems to quadratic-bilinear systems and develop a greedy-type framework to select a good choice of interpolation points for the construction of the projection matrices. The results are compared with standard quadratic-bilinear projection methods and we observe that the approximations obtained by the proposed method yield high accuracy.

中文翻译：

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使用误差边界的二次双线性系统模型降阶的多元矩匹配

我们提出了一种自适应矩匹配框架，用于二次双线性系统的模型降阶。在这个框架中，一个重要的问题是选择那些要实现时刻匹配的移位频率。到目前为止，选择通常是随机的或与非线性系统的线性部分有关。在本文中，我们将一般线性时不变系统的现有后验误差界的使用扩展到二次双线性系统，并开发了一个贪心型框架来选择一个好的插值点来构建投影矩阵。将结果与标准二次双线性投影方法进行比较，我们观察到通过所提出的方法获得的近似值具有很高的准确性。