Abstract Model parameter estimation, model order selection, variable selection and time delay estimation are four important issues that receive increasing interests in dynamic system identification. However, previous work did not solve the four issues simultaneously. Motivated by the multiple kernel-based regularization method (MKRM), this paper proposes a new multiple kernel-based regularization method for joint model parameter estimation, model order selection, variable selection and time delay estimation for delay linear dynamic systems, referred to as the MKRM-D. Then, an efficient iterative reweighted algorithm is derived to solve the resulting difference of convex functions programming (DCP) problem. In addition, by exploiting the structure of the objective function in each iteration of this algorithm, the alternating direction method of multipliers (ADMM) is employed to decompose the centralized problem into a series of independent subproblems with lower variable dimension, which can be solved in a parallel and distributed manner. The performance of the proposed method is demonstrated by numerical experiments using both synthetic and real data.

中文翻译：

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一种新的基于多核正则化的时滞线性动态系统辨识方法

摘要 模型参数估计、模型阶数选择、变量选择和时延估计是动态系统辨识中越来越受关注的四个重要问题。然而，之前的工作并没有同时解决这四个问题。受多核正则化方法（MKRM）的启发，本文提出了一种新的多核正则化方法，用于时滞线性动态系统的联合模型参数估计、模型阶数选择、变量选择和时滞估计，称为MKRM-D。然后，推导出一种有效的迭代重加权算法来解决由此产生的凸函数规划（DCP）问题的差异。此外，通过利用该算法每次迭代中目标函数的结构，采用乘法器交替方向法（ADMM）将集中问题分解为一系列具有较低可变维数的独立子问题，这些子问题可以并行分布式求解。通过使用合成数据和真实数据的数值实验证明了所提出方法的性能。