Realization and Subspace Identification of Continuous-Time Stochastic Systems

在标准的系统辨识中，由于被控对象的输入输出数据是以数字方式采样、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识别质量、弹簧常数和阻尼因子，因为大多数物理系统在时间上是连续的。这一事实激发了连续时间系统辨识的最新发展。首先给出了连续时间随机系统的近似δ-算子模型，然后给出了δ-算子新息模型。然后，将MOESP型子空间辨识方法应用于新息模型，得到了一种新的连续时间系统的子空间辨识方法。此外，工具矩阵的引入，以提高识别模型的准确性。仿真结果包括在内。这些结果在第31届ISCIE随机系统研讨会（1999）上发表，并发表在《ISCIE学报》（2001）上。在控制器已知的假设下，我们将上述基于δ算子的方法应用于连续时间闭环系统的辨识。基于对偶尤拉参数化，将闭环辨识问题转化为被控对象联合输入输出过程的等效开环辨识问题。所需的开环传递矩阵的估计代数来自联合过程的状态空间模型。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，该技术可用于不稳定对象的辨识。研究结果已在第三届亚洲控制会议（2000年）上公布。基于δ-算子逼近，利用改进的椭球定界技术，导出了连续时间随机系统的模型集辨识方法。研究结果发表在《国际化学品分类学报》（1999年）上。

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).