Model Reduction by Moment Matching for Linear and Nonlinear Systems
Model Reduction by Moment Matching for Linear and Nonlinear Systems
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DOI：
10.1109/tac.2010.2046044
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发表时间：
2010-10-01
影响因子：
6.8
通讯作者：
Astolfi, Alessandro
中科院分区：
文献类型：
--
作者：
Astolfi, Alessandro
利用矩的概念讨论了（单输入，单输出）线性和非线性系统的模型降阶问题。重新访问的线性理论允许获得新的结果，线性系统和发展的非线性增强的概念的时刻。反过来，这是用来构成和解决的模型简化问题的时刻匹配的非线性系统，开发一个概念的非线性系统的频率响应，并解决模型简化问题的约束条件下存在的简化模型。所提出的结果，投影方法，协方差扩展问题和插值理论之间的连接。最后，通过简单的算例和案例分析对理论进行了说明。
The model reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the model reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve model reduction problems in the presence of constraints on the reduced model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies.