Stochastic Subspace Identification Method and its Applications to Closed-Loop Identification

本研究的目的是发展多变量时间序列的随机实现方法，进而获得闭环系统的随机子空间辨识算法。1.在文献[1]中，我们利用典型相关分析(CCA)发展了一种新的随机实现算法，从而在由二阶平稳随机过程生成的Hilbert空间中通过LQ分解得到了前向新息模型。在文[2]中，我们回顾了一种计算平稳随机过程的未来和过去之间的典型相关性的方法，并回顾了条件CCA在存在外源输入的随机系统实现中的应用。2.出版了一本关于随机实现的书[3](日文)。3.结合基于正交分解的方法和加权LQ分解，我们发展了…的一个子空间恒等式具有观测离群点的线性随机系统的更多离子方法[4]。利用ORT方法和一种简单的基于残差中值的稳健统计方法对观测输出序列中的野值进行检测。4.在联合输入输出方法的框架下，提出了一种连续时间对象闭环系统的子空间辨识方法。首先利用对象的对偶Youla参数化得到等价的开环问题，然后推导出基于Delta算子的IV-MOESP类型子空间辨识算法。通过对一个化工对象模型的仿真研究，验证了该方法的可行性。5.在文[6]中，提出了一种基于ORT方法的子空间辨识方法，用于辨识闭环系统中被控对象和控制器的状态空间模型。文中还详细讨论了输入信号在闭环辨识中的作用。由于所得到的模型是高阶的，所以使用一种称为SR方法的模型降阶过程来获得低维模型。6.通过使用EM算法，我们发展了一种方法，在存在观测离群点的情况下改进用子空间辨识方法获得的状态空间模型的估计[7]。EM算法通过两种子空间辨识方法进行初始化：MOESP和ORT。数值算例表明，EM算法能够单调地改进子空间辨识方法得到的初值。较少

The objective of this research is to develop stochastic realization methods for multivariate time-series and then to obtain some stochastic subspace identification algorithms for closed-loop systems. The following are the results of the research in the past two years.1.In [1], we have developed a new stochastic realization algorithm using canonical correlation analysis(CCA), thereby deriving the forward innovation model by means of LQ decomposition in a Hilbert space generated by second order stationary stochastic processes. In [2], we have reviewed a method of computing the canonical correlations between the future and past of a stationary stochastic process, and also reviewed an application of conditional CCA to the realization of stochastic systems in the presence of exogenous inputs.2.A book on stochastic realization is published [3] (in Japanese).3.By combining the orthogonal decomposition (ORT)-based method and a weighted LQ decomposition, we have developed a subspace identificat … More ion method for a linear stochastic system subjected to observation outliers [4]. Outliers in observed output sequence are detected by busing the ORT-method and a simple scheme in robust statistics based on the median of residuals.4.A subspace identification method for a continuous-time plant operating in closed-loop is developed in the framework of the joint input-output approach. We first obtain an equivalent open-loop problem by using the dual Youla parameterization of the plant, and then derived a delta-operator based IV-MOESP type subspace identification algorithm. Simulation studies by using a chemical plant model show the feasibility of the method [5].5.In [6], a subspace identification method of identifying state space models of the plant and controller operating in a closed-loop by using the ORT method. We have also discussed the role o f input signals in closed-loop identification in detail. Since the obtained models are of higher order, a model reduction procedure called SR method is employed to get lower dimensional models.6.By using the EM algorithm, we have developed a method of improving estimates of a state space model obtained by subspace identification methods in the presence of observation outliers [7]. The EM algorithm is initialized by two subspace identification methods : MOESP and ORT. Numerical examples show that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods. Less