Excitation-Oriented Recursive Learning Control

To address the severe dependence on the high-level persistent excitation (PE) condition and the performance deficiencies in traditional stochastic gradient descent-based neural network learning control (SGD-NNLC), which is grounded in deterministic learning theory, we proposed a novel online learning framework for neural networks named excitation-oriented recursive learning control (EORLC). EORLC employs excitation-oriented forgetting recursive least squares (EOFRLS) to guide the weight update laws of radial basis function neural networks (RBFNNs). The forgetting factor is allocated based on the PE level and error at each time point along the training trajectory, thereby enabling the RBFNN to achieve superior learning performance. Finally, this paper theoretically proves the exponential stability of the closed-loop system of EORLC under the PE condition. Experimental validation conducted on a computer numerical control machine tool confirms the superiority of this learning control algorithm over SGD-NNLC in terms of learning performance.