Identification of Feedback and Nonlinear Systems by using Subspace Methods

基于1996年提出的正交分解（ORT）方法，在可测扰动存在的假设下，提出了一种新的闭环子空间辨识算法，并对仿真和工业数据进行了数值计算。我们还考虑了一个基于LQ分解的子空间识别方法，用于识别组合确定性随机系统的随机部分，表明随机部分是通过使用单一的LQ分解的假设下，过去的地平线是足够大的。这一结果补充了著名的MOESP方法，其中随机部分的识别已被忽略了多年。针对非线性动力系统的辨识问题，采用Hammerstein系统和线性系统交替辨识的方法，推导出了一种辨识两个线性系统夹着一个静态非线性项的Wiener-Hammerstein系统的方法，其中采用基于数据驱动的局部坐标梯度法来最小化输出误差.基准问题的算法和数值结果在SYSID 2009，圣马洛的特别会议。

Based on the orthogonal decomposition (ORT) method 1996, we have developed a new closed loop subspace identification algorithm under the assumption that measurable disturbances are available, and obtained successful numerical results for both simulated and industrial data. We have also considered an LQ decomposition based subspace identification method for identifying the stochastic part of a combined deterministic stochastic system, showing that the stochastic part is derived by using a single LQ decomposition under the assumption that the past horizon is sufficiently large. This result complements the well-known MOESP method, for which the identification of stochastic part has been ignored for many years. Concerning the identification of nonlinear dynamical systems, a method of identifying Wiener-Hammerstein systems, in which a static nonlinearity is sandwiched by two linear systems, is derived by using a method of alternately identifying Hammerstein system and a linear system, where the data driven local coordinate-based gradient method is used for minimizing output errors. The algorithm and numerical results for the benchmark problem are presented at the special session of SYSID 2009, Saint-Malo.