IEEE Trans Cybern. 2022 Oct;52(10):10800-10813. doi: 10.1109/TCYB.2021.3066639. Epub 2022 Sep 19.
This article proposes an effective optimal bounded ellipsoid (OBE) identification algorithm for neural networks to reconstruct the dynamics of the uncertain Euler-Lagrange systems. To address the problem of unbounded growth or vanishing of the learning gain matrix in classical OBE algorithms, we propose a modified OBE algorithm to ensure that the learning gain matrix has deterministic upper and lower bounds (i.e., the bounds are independent of the unpredictable excitation levels in different regressor channels and, therefore, are capable of being predetermined a priori). Such properties are generally unavailable in the existing OBE algorithms. The upper bound prevents blow-up in cases of insufficient excitations, and the lower bound ensures good identification performance for time-varying parameters. Based on the proposed OBE identification algorithm, we developed a closed-loop controller for the Euler-Lagrange system and proved the practical asymptotic stability of the closed-loop system via the Lyapunov stability theory. Furthermore, we showed that inertial matrix inversion and noisy acceleration signals are not required in the controller. Comparative studies confirmed the validity of the proposed approach.
本文提出了一种有效的神经网络最优有界椭球（OBE）辨识算法，用于重构不确定的欧拉-拉格朗日系统的动态。为了解决经典 OBE 算法中学习增益矩阵的无界增长或消失的问题，我们提出了一种改进的 OBE 算法，以确保学习增益矩阵具有确定的上界和下界（即，界限与不同回归器通道中的不可预测的激励水平无关，因此可以预先确定）。这些特性在现有的 OBE 算法中通常是不可用的。上界可防止激励不足时的爆炸，下界确保了时变参数的良好辨识性能。基于提出的 OBE 辨识算法，我们为 Euler-Lagrange 系统开发了一个闭环控制器，并通过 Lyapunov 稳定性理论证明了闭环系统的实际渐近稳定性。此外，我们表明控制器中不需要惯性矩阵反转和噪声加速度信号。比较研究证实了所提出方法的有效性。
