New Development in Subspace System Identification via Realization Theory

本研究计画的目标是发展新的子空间辨识方法，以多变量系统的确定性与随机性实现理论为基础。以下是过去三年的研究结果。通过证明L-矩阵的每一列是由给定的输入输出数据生成的一对输入输出向量[R6，R8]，阐明了LQ分解在子空间方法中的作用.利用联合输入输出法[J1]和两阶段法[J5，R1]，分别推导了基于正交分解的子空间辨识算法。并将两阶段法应用于工业过程辨识[R5].利用Hilbert空间中的LQ分解，导出了一种新的随机实现算法[J3]，并成功地应用于闭环随机实现[R7]。此外，还分析了有限区间随机平衡实现算法，并证明了在有限协方差序列存在的假设下，有限区间平衡实现算法能提供稳定的最小相位模型[J 4，R2].利用J-谱分解和H-无穷辨识技术[R4，R9]，给出了含变量误差模型的辨识方法。此外，为了科普观测数据中的异常值，本文还将EM算法与ORT方法相结合，提出了新的识别算法[J2，R3]. Springer-Verlag出版了一本关于系统辨识的子空间方法的英文专著，它适合于研究生和应用科学家的教科书[B1]。

The objective of this research project is to develop new subspace identification methods for multivariable systems based on deterministic and stochastic realization theories. The following are the results of the research for the last three years.1. The role of LQ decomposition in subspace methods is clarified by showing that each column of L-matrix is a pair of input-output vectors generated by given input-output data [R6, R8].2. Subspace identification algorithms of identifying closed-loop systems are derived using the ORT (orthogonal decomposition based subspace identification) method by using joint input-output approach [J1] and by the two-stage method [J5, R1]. Moreover, the two stage method is applied to the identification of industrial process [R5].3. Anew stochastic realization algorithm is derived by using LQ decomposition in Hilbert space [J3], and it is successfully applied to the closed-loop stochastic realization [R7]. Also, a finite-interval stochastic balanced realization is analyzed and it is shown that the finite-interval balanced realization algorithm provides stable minimum-phase models under the assumption that an exact finite covariance sequence is available [J4, R2].4. Identification methods for error-in-variables models are developed by using J-spectral factorization And H-infinity identification technique [R4, R9]. Moreover, new identification algorithms are derived by combining the EM algorithm and ORT method in order to cope with outliers in observed data [J2, R3].5. An English monograph for subspace methods for system identification is published from Springer-Verlag, which is suitable for a textbook of graduate students and of applied scientists [B1].