Realization and Subspace Identification of Continuous-Time Stochastic Systems

在标准系统辨识中，由于工厂输入输出数据是数字化采样、存储和处理的，因此通常采用离散时间模型。然而，对于机械系统，有必要在连续时间模型中确定质量、弹簧常数和阻尼系数，因为大多数物理系统在时间上是连续的。这一事实推动了连续时间系统识别的最新发展。1．我们推导了一个近似的 δ 算子模型，然后推导了连续时间随机系统的 δ 算子创新模型。然后，将MOESP型子空间辨识方法应用到创新模型中，得到了一种新的连续时间系统子空间辨识方法。此外，引入仪器矩阵以提高识别模型的准确性。包括模拟结果。这些结果在第 31 届 ISCIE 随机系统研讨会（1999 年）上发表，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。基于对偶Youla参数化，将被控对象联合输入输出过程的闭环辨识问题转化为等效的开环辨识问题。所需开环传递矩阵的估计是从联合过程的状态空间模型以代数方式导出的。应当注意，本技术可以用于控制器的知识可用的情况。仿真结果表明，该技术适用于不稳定植物的识别。结果在第三届亚洲控制会议（2000）上公布。3．基于δ算子近似，我们推导了一种利用改进的椭球有界技术来识别连续时间随机系统的模型集的方法。结果发表在 Trans. 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).