Wang Zishuo, Chen Beichen, Sun Hongliang, Liang Shuning
School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin, 132022, China.
School of Energy and Power Engineering, Northeast Electric Power University, Jilin, 132012, China.
Sci Rep. 2024 Dec 28;14(1):30802. doi: 10.1038/s41598-024-81423-w.
This paper proposes a joint multi-innovation fractional gradient descent identification algorithm for fractional order systems. First, the flexibility of fractional calculus is leveraged to design a joint fractional gradient descent algorithm capable of estimating system parameters and unknown orders. The estimated system parameters are used as the initial conditions to identify the unknown order, and the identified order is used as the update conditions for the system parameters. Through the joint iteration of two fractional order gradients, both the identified order and parameters are updated. In addition, multi-innovation theory is applied to extend the joint fractional gradient descent algorithm to a joint multi-innovation fractional gradient descent algorithm, which improves the system identification accuracy. Then, the convergence of the algorithm is theoretically analyzed. Finally, the effectiveness of the algorithm is verified through numerical simulation and an experiment on the identification of an actual flexible linkage system.
本文提出了一种用于分数阶系统的联合多新息分数梯度下降辨识算法。首先，利用分数阶微积分的灵活性设计了一种能够估计系统参数和未知阶数的联合分数梯度下降算法。将估计出的系统参数用作识别未知阶数的初始条件，而识别出的阶数用作系统参数的更新条件。通过两个分数阶梯度的联合迭代，同时更新识别出的阶数和参数。此外，应用多新息理论将联合分数梯度下降算法扩展为联合多新息分数梯度下降算法，提高了系统辨识精度。然后，从理论上分析了该算法的收敛性。最后，通过数值仿真和对实际柔性连杆系统辨识的实验验证了该算法的有效性。
