基于非均匀采样数据的连续时间系统辨识研究

This project investigates control-oriented identification of industrial processes from irregularly sampled data. Two issues related to this problem are considered, namely: (1) Optimal identification in the presence of colored noise, where optimal means that the model parameter estimates are unbiased and have minimum variance. To this end, most available methods identify discrete-time models of colored noise and apply them to prewhiten the colored noise to achieve the conditions for optimal parameter estimation. However, the traditional treatment is not suitable for irregular sampling since the obtained noise models are typically time varying. To avoid this difficulty, we suggest to model the plant and noise processes in the continuous-time domain, since continuous-time model parameters are independent of sampling period. The main task in this work is to solve the problem of continuous-time noise model identification, and to show the advantages of irregular sampling compared with traditional regular sampling; (2) Time delay system identification. Time delay is an important feature of most physical processes. The use of time delay models has been a common practice to obtain better representations of these processes. By injecting a pure time delay to a linear model, the sluggish property of the system can be well described. A time delay model is generally more difficult to identify due to the nonlinearity introduced by the time delay. The initialization is a critical issue since the loss function is usually multi-modal and local convergence is a common problem. To make the initialization easier, we present several guidelines for the choice of initial parameters, and possible approaches to smooth the loss function shapes. The project aims to enrich the existing theory on industrial process identification, contributing more identification methods to industrial process identification and control design technology under irregular sampling.

本项目围绕非均匀采样和连续时间系统辨识，开展对以下两个科学问题的研究：(1)抗扰辨识，研究在有色噪声干扰下获得系统传递函数模型参数无偏最小方差估计的新方法。为了在非均匀采样下得到时不变模型，提出在连续时间域内对系统进行建模。重点研究辨识连续噪声模型的有效方法，探讨并证明非均匀采样在提高参数估计收敛性能方面的优越之处。讨论如何将连续噪声模型辨识算法与传统辨识算法相结合进而辨识连续Box-Jenkins模型，为非均匀采样系统的控制器设计提供更准确的模；(2)时滞系统辨识，辨识带时滞参数的连续传递函数模型，以实现对大时滞系统动态响应特性更为准确的描述。针对时滞估计中存在的局部收敛问题，提出一系列方法来平滑目标函数，增强算法对初始参数选择的鲁棒性，提高时滞估计的全局收敛性能。本项目成果将进一步丰富现有的工业过程辨识理论，对于提高非均匀采样下工业过程辨识建模和控制技术水平具重要参考意义。

许多实际系统带有固有的时延。准确地估计时延和系统模型参数对于系统分析，预测或控制设计非常重要。但时延的非线性特性使得模型辨识问题更具挑战性，导致模型参数估计容易陷入局部最优。本项目提出了几种辨识方法用于解决时延系统辨识问题，并对算法进行的深入的理论分析，详细阐述了如何将提出的算法用于无线电能传输系统建模。仿真和实验验证结果表明，提出的方法能够很好的处理多(单)输入单输出、时变参数系统辨识问题。