Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems
Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems
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DOI：
10.1109/tac.2014.2370271
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发表时间：
2015-04
影响因子：
6.8
通讯作者：
T. Ishizaki;H. Sandberg;K. Kashima;J. Imura;K. Aihara
中科院分区：
文献类型：
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作者：
T. Ishizaki;H. Sandberg;K. Kashima;J. Imura;K. Aihara
我们提出了一种用于分布式控制系统的耗散性保持结构化模型简化方法。作为开发结构化模型简化的基本工具，我们首先在奇异扰动近似的基础上为一般线性系统建立耗散性保持模型简化。为此，通过推导奇异扰动模型的易于处理的表达式，我们用存储函数的投影式变换来表征耗散性保持，并且我们表明所得到的近似误差与索引矩阵的被忽略的特征值之和相关。接下来，利用这种耗散性保持模型简化，我们开发了一种用于分布式控制系统的结构化控制器简化方法。该方法的主要意义是保留耗散控制器的空间分布，并根据 H2 范数为闭环系统的性能退化提供先验界限。通过互联二阶系统振动抑制控制的数值算例验证了该方法的有效性。
We propose a dissipativity-preserving structured model reduction method for distributed control systems. As a fundamental tool to develop structured model reduction, we first establish dissipativity-preserving model reduction for general linear systems on the basis of a singular perturbation approximation. To this end, by deriving a tractable expression of singular perturbation models, we characterize dissipativity preservation in terms of a projection-like transformation of storage functions, and we show that the resultant approximation error is relevant to the sum of neglected eigenvalues of an index matrix. Next, utilizing this dissipativity-preserving model reduction, we develop a structured controller reduction method for distributed control systems. The major significance of this method is to preserve the spatial distribution of dissipative controllers and to provide an a priori bound for the performance degradation of closed-loop systems in terms of the H2-norm. The efficiency of the proposed method is verified through a numerical example of vibration suppression control for interconnected second-order systems.