子空间模型辨识方法综述

Overview on subspace model identification methods

作为传统线性系统辨识方法的一个有益补充,子空间模型辨识方法(SMI)近年来获得了广泛关注.这类方法综合了系统理论,线性代数和统计学三方面的思想,其特点是直接由输入输出数据辨识系统的状态空间模型,因而非常适合多变量系统辨识.首先介绍了SMI的基本思想,然后分析了3种基本算法(N4SID、MOESP和CVA)的异同点、算法实现、统计特性和模型稳定性等方面.随后探讨了其他一些SMI算法,包括连续时间系统SMI算法、频域SMI算法、闭环SMI算法和非线性系统SMI算法.为说明SMI方法的特性,通过一个工厂实际例子研究对比了3种SMI基本算法和一种传统辨识算法———预测误差方法(PEM).最后阐述了理论方面有待进一步研究的主要问题.

As a useful complement to the classical linear system identification methods, the subspace model identification （SMI） methods have drawn much research attention recently. Based on input-output data, state space models are directly identified by the SMI methods combined with the system theory, linear algebra and statistics. In this paper, basic idea of SMI methods is presented at first. Then three basic algorithms, i.e., N4SID, MOESP and CVA, are discussed in terms of difference and similarity, implementation, statistical features and model stability. Some other SMI methods are subsequently reviewed such as the SMI methods for continuous time systems, the frequency domain SMI methods, the closed-loop SMI methods and SMI methods for nonlinear systems. In order to demonstrate the features of SMI methods, comparison between the SMI methods and the prediction error methods （PEM） is made based on the same data sets collected from real-life application. Finally, some further theoretical problems are discussed.