Model reduction and system identification for master equation control systems
Model reduction and system identification for master equation control systems
复制标题
主方程控制系统的模型简化和系统辨识
DOI：
10.1109/acc.2003.1244099
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
R. Murray
中科院分区：
文献类型：
--
作者：
M. Gallivan;R. Murray
主方程描述概率分布的连续时间演化，其特征是简单的双线性结构和通常的高维。我们开发了一种模型约简方法，通过去除不可能的配置和分组相似的配置来减少可能配置的数量和相应的维数。减少的误差范围是基于兴趣的最小和最大时间尺度导出的。然后给出了一个类似的线性辨识过程，该过程计算一个预定组态集的状态矩阵和输出矩阵。这些思想首先在受表面演化问题启发的有限维模型中得到证明，然后在无限维薄膜生长主方程中得到证明。
A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear-like structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite-dimensional film growth master equation.