This study proposes two improved gradient descent parameter estimation algorithms for rational state-space models with time-delay. These two algorithms, based on intelligent search method and momentum method, can simultaneously estimate the time-delay and parameters without the matrix eigenvalue calculation in each iteration. Compared with the traditional gradient descent algorithm, the improved algorithms come with two advantages: having quicker convergence rates and less computational efforts, particularly meaningful for those large-scale systems. A simulated example is selected to illustrate the efficiency of the proposed algorithms.

中文翻译：

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时滞有理状态空间系统的改进的梯度下降算法：智能搜索法和动量法

这项研究为带时滞的有理状态空间模型提出了两种改进的梯度下降参数估计算法。这两种算法基于智能搜索法和动量法，可以同时估计时间延迟和参数，而无需在每次迭代中计算矩阵特征值。与传统的梯度下降算法相比，改进后的算法具有两个优点：收敛速度更快，计算量更少，这对那些大型系统特别有意义。选择一个仿真示例来说明所提出算法的效率。