Optimization of Persistent Excitation Level of Training Trajectories in Deterministic Learning
研究了确定性学习中持续激励水平与输入信号的显式关系，提出生成训练轨迹的方法以提升RBF神经网络的特征信息，并通过三轴数控机床实验验证了该方法能显著降低跟踪误差和轮廓误差。
When the persistent excitation (PE) condition is met, neural network control based on deterministic learning can approximate the true dynamics of nonlinear systems. However, in this approach, learning speed and accuracy are severely constrained by the PE level. In this article, we investigate the explicit relationship between the PE level and input signals. Specifically, this research investigates a neural network structure determined by the mechanical characteristics of a computer numerical control (CNC) machine tool. We explore a method to generate training trajectories that fill the designated feature space or repeatedly pass through hidden layer nodes, ensuring that deterministic learning achieves a sufficient PE level. Then, we validated the effectiveness of the proposed method through experiments conducted on a three-axis CNC machine tool using actual machining trajectories. The experimental results consistently confirmed that the generated training trajectories endow the RBF neural network with more feature information than random NURBS trajectories. Additionally, the tracking error and contour error of the CNC machine tool were significantly reduced.