When is the discretization of a spatially distributed system good enough for control?
When is the discretization of a spatially distributed system good enough for control?
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空间分布式系统的离散化何时足以进行控制？
DOI：
10.1016/j.automatica.2010.06.001
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
E. Kerrigan
中科院分区：
文献类型：
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作者：
B. Jones;E. Kerrigan
本文描述了一种基于空间离散化技术获得的低阶模型来控制空间分布的植物的新的、直接的方法。适当的离散化水平是通过计算连续更精细的空间分辨率的加权模型之间的ν-间隙序列，并用另一序列与解析级数限定来确定的。证明了这样的级数在初始序列中的加权模型和空间分布的加权对象之间的ν间隙上形成了一个上界。这使得能够在低阶模型上综合保证稳定实际对象的鲁棒控制器，这是大多数模型降阶方法所不具有的特征，其中高阶模型和被控对象之间的差距通常是未知的，并且高阶模型和降阶模型之间的差距可能太昂贵而无法计算。由于当前界的计算是基于小状态维加权模型的，新方法避免了基于大规模模型降阶的方法所固有的数值问题。本文的思想在一维热传导方程的扰动抑制问题上得到了验证。
This paper describes a new and straightforward method for controlling spatially distributed plants based on low-order models obtained from spatial discretization techniques. A suitable level of discretization is determined by computing the sequence of ν-gaps between weighted models of successively finer spatial resolution, and bounding this by another sequence with an analytic series. It is proved that such a series forms an upper bound on the ν-gap between a weighted model in the initial sequence and the spatially distributed weighted plant. This enables the synthesis, on low-order models, of robust controllers that are guaranteed to stabilize the actual plant, a feature not shared by most model reduction methods where the gap between the high-order model and plant is often not known, and where the gap between high-order and reduced models may be too expensive to compute. Since the calculation of the current bound is based on weighted models of small state-dimension, the new method avoids the numerical problems inherent in large-scale model reduction based approaches. The ideas presented in this paper are demonstrated on a disturbance rejection problem for a 1D heat equation.