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| Subspace-based identification of discrete time-delay system |
| Qiang Liu, Jia-chen Ma |
| School of Astronautics, Harbin Institute of Technology, Harbin 150001, China; School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai 264209, China |
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Abstract We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.
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Received: 23 October 2015
Published: 06 June 2016
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基于子空间的离散时滞系统辨识
目的：时滞存在于很多系统中，时滞会导致系统性能下降并使系统变得不稳定。因此研究具有未知时滞的线性辨识对于系统分析和控制设计有着很重要的作用。本文提出了一种ACS算法，用来解决具有单一时延的离散随机时滞系统的辨识。
创新点：提出一种ACS算法，将时滞系统矩阵从估计的增广矩阵中重新恢复出来。采用状态增广方法将时滞系统与等价的线性时不变系统联系起来，利用N4SID算法对增广系统矩阵进行初始估计。
方法：时滞系统被表达为具有单一时延的时滞差分方程。首先利用状态增广方法将线性时滞系统转化为一个等价的线性时不变系统。然后利用子空间辨识方法对增广系统矩阵进行初始估计，提出了一种ACS算法，得到了线性时滞系统的状态空间模型。最后通过解决两个最小二乘法问题，利用卡尔曼状态序列和输入输出数据得到相同状态空间下的时滞系统矩阵。
结论：本文提出的ACS算法可以利用估计的增广矩阵得出时滞系统矩阵，解决了线性离散时滞系统的辨识问题，同时证明了该算法具有良好的局部收敛性能。仿真结果表明了这种算法的有效性。
关键词：
辨识问题,
时滞系统,
子空间辨识方法,
ACS算法,
最小二乘法
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