改进的梯度下降法在离散时滞系统中的应用

Application of an improved stochastic gradient method in discrete-time system with time-delay

提出了离散时滞系统的辨识问题,这个问题包括时滞参数的辨识和系统动态参数的辨识。提出了一种基于辅助模型思想和低通滤波技术的带可变遗忘因子的随机梯度下降法对系统时滞参数和系统动态参数同时进行在线辨识。建立辅助模型,用辅助模型输出代替系统的无噪声输出。引入基于预测误差的可变遗忘因子,加快算法的收敛速度,提高算法的预测精度。同时,引入低通滤波技术增大时滞参数的收敛域,使得损失函数取得全局最优。最后,通过仿真证明了本文算法的有效性。

In this paper ,the problem of identification of discrete‐time system with a time‐delay is addressed .This problem involves both the estimation of the time‐delay and the estimation of the dynamic parameters .An Improved Stochastic Gradient Descent Method based on auxiliary model theory and low‐pass filtering technique with a variable forgetting fac‐tor is proposed to simultaneously estimate the time‐delay and dynamic parameters on line .An auxiliary model is estab‐lished to estimate the noise‐free output of system .A variable forgetting factor based on prediction error is introduced to enhance the convergence rate and identification accuracy .Moreover ,a low‐pass filtering technique is used to widen the convergence region and the sharp peaks of cost function are ‘spread out’ ,w hich makes the global minimum easier to reach .Simulation results are included to show the effectiveness of the proposed method .