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.

中文翻译：

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具有确定性和有界学习增益的最佳有界椭球体识别：Euler-Lagrange系统的设计和应用。

本文提出了一种有效的神经网络最优有界椭球（OBE）识别算法，以重构不确定的Euler-Lagrange系统的动力学。为了解决经典OBE算法中学习增益矩阵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性的上下限（即，边界独立于不可预测的激励水平）在不同的回归通道中，因此能够事先确定。此类属性通常在现有的OBE算法中不可用。上限防止在激励不足的情况下爆裂，下限确保对随时间变化的参数具有良好的识别性能。基于提出的OBE辨识算法，我们为Euler-Lagrange系统开发了一种闭环控制器，并通过Lyapunov稳定性理论证明了该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求逆和有噪加速度信号。比较研究证实了该方法的有效性。