Realization and Subspace Identification of Continuous-Time Stochastic Systems

在标准系统辨识中，通常采用离散时间模型，因为工厂的输入输出数据是数字化采样、存储和处理的。然而，对于机械系统，由于大多数物理系统在时间上是连续的，因此有必要在连续时间模型中识别质量、弹簧常数和阻尼因子。这一事实促使了最近连续时间系统辨识的发展。首先导出连续时间随机系统的近似δ算子模型，然后导出连续时间随机系统的δ算子创新模型。然后，将moesp型子空间识别方法应用于创新模型，得到了一种新的连续时间系统子空间识别方法。此外，为了提高识别模型的准确性，还引入了仪器矩阵。最后给出了仿真结果。这些结果发表在第31届ISCIE随机系统研讨会（1999）上，并发表在Trans上。ISCIE(2001)。2。在控制器已知的情况下，我们将上述基于δ算子的技术应用于连续时间闭环系统的辨识。基于双Youla参数化，将闭环辨识问题转化为对象联合输入输出过程的等效开环辨识问题。从联合过程的状态空间模型出发，用代数方法得到了期望开环传递矩阵的估计。应当注意的是，本技术可用于控制器知识可用的情况。仿真结果表明，该方法可用于不稳定对象的识别。研究结果发表在第三届亚洲控制会议（2000）上。在δ算子近似的基础上，利用改进的椭球边界技术，导出了一种连续时间随机系统的模型集辨识方法。研究结果发表在《Trans》杂志上。ISCIE(1999)。

In standard system identification, the discrete-time models are commonly employed since the plant input-output data are sampled, stored and processed digitally. For mechanical systems, however, it is necessary to identify mass, spring constant and damping factor in the continuous-time model, since most physical systems are continuous in time. This fact motivates recent development in continuous-time system identification.1. We derive an approximate δ-operator model and then the δ-operator innovation model for a continuous-time stochastic system. Then, applying the MOESP-type subspace identification method to the innovation model, we have obtained a new subspace identification method for a continuous-time system. Moreover, the instrumental matrix is introduced in order to improve the accuracy of the identified models. Simulation results are included. These results are presented at the 31st ISCIE Stochastic System Symposium (1999) and published in Trans. ISCIE (2001).2. We applied the above δ-operator based technique to the identification of a continuous-time closed-loop system under the assumption that the controller is known. Based on the dual Youla parametrization, the closed-loop identification problem is transformed to an equivalent open-loop identification for the joint input-output process of the plant. The estimate of the desired open-loop transfer matrix is algebraically derived from the state-space model of the joint process. It should be noted that the present technique can be used for the case where the knowledge of controller is available. Simulation results shows that the present technique is applied to the identification of unstable plant. The result is presented at the 3rd Asian Control Conference (2000).3. Based on the δ-operator approximation, we have derived a method of model set identification for a continuous-time stochastic system by using the modified ellipsoidal bounding technique. The result is published in Trans. ISCIE (1999).