Memory, as the basis of learning, determines the storage, update and forgetting of knowledge and further determines the efficiency of learning. Featured with the mechanism of memory, a radial basis function neural network based learning control scheme named real-time progressive learning (RTPL) is proposed to learn the unknown dynamics of the system with guaranteed stability and closed-loop performance. Instead of the Lyapunov-based weight update law of conventional neural network learning control (NNLC), which mainly concentrates on stability and control performance, RTPL employs the selective memory recursive least squares (SMRLS) algorithm to update the weights of the neural network and achieves the following merits: 1) improved learning speed without filtering, 2) robustness to hyperparameter setting of neural networks, 3) good generalization ability, i.e., reuse of learned knowledge in different tasks, and 4) guaranteed learning performance under parameter perturbation. Moreover, RTPL realizes continuous accumulation of knowledge as a result of its reasonably allocated memory while NNLC may gradually forget knowledge that it has learned. Corresponding theoretical analysis and simulation studies demonstrate the effectiveness of RTPL.

翻译：记忆作为学习的基础，决定了知识的存储、更新与遗忘，并进一步影响学习效率。本文提出一种具有记忆机制的径向基函数神经网络学习控制方案——实时渐进学习（RTPL），用于在保证系统稳定性与闭环性能的前提下学习系统的未知动力学。与传统神经网络学习控制（NNLC）基于李雅普诺夫方法的权重更新律（主要关注稳定性与控制性能）不同，RTPL采用选择性记忆递归最小二乘（SMRLS）算法更新神经网络权重，并实现了以下优势：1）无需滤波即可提升学习速度；2）对神经网络超参数设置具有鲁棒性；3）良好的泛化能力，即可在不同任务中复用已学知识；4）在参数扰动下仍能保证学习性能。此外，RTPL因其合理分配的记忆机制实现了知识的持续积累，而NNLC可能逐渐遗忘已学知识。相应的理论分析与仿真研究验证了RTPL的有效性。