Optimization of Persistent Excitation Level of Training Trajectories in Deterministic Learning

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.