Memory, as the basis of learning, determines the storage, update and forgetting of the knowledge and further determines the efficiency of learning. Featured with a mechanism of memory, a radial basis function neural network (RBFNN) 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 stochastic gradient descent (SGD) update law in adaptive neural control (ANC), RTPL adopts the selective memory recursive least squares (SMRLS) algorithm to update the weights of the RBFNN. Through SMRLS, the approximation capabilities of the RBFNN are uniformly distributed over the feature space and thus the passive knowledge forgetting phenomenon of SGD method is suppressed. Subsequently, RTPL achieves the following merits over the classical ANC: 1) guaranteed learning capability under low-level persistent excitation (PE), 2) improved learning performance (learning speed, accuracy and generalization capability), and 3) low gain requirement ensuring robustness of RTPL in practical applications. Moreover, the RTPL based learning and control will gradually reinforce each other during the task execution, making it appropriate for long-term learning control tasks. As an example, RTPL is used to address the tracking control problem of a class of nonlinear systems with RBFNN being an adaptive feedforward controller. 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，进而决定了学习效率。本文提出一种具有记忆机制的基于径向基函数神经网络（RBFNN）的学习控制方案——实时渐进学习（RTPL），用于在保证系统稳定性和闭环性能的前提下学习未知系统动力学。与传统自适应神经控制（ANC）中采用的随机梯度下降（SGD）更新律不同，RTPL采用选择性记忆递归最小二乘（SMRLS）算法更新RBFNN的权值。通过SMRLS，RBFNN的逼近能力在特征空间上均匀分布，从而抑制了SGD方法中的被动知识遗忘现象。随后，相较于经典ANC，RTPL实现了以下优势：1）在低水平持续激励（PE）条件下保证学习能力；2）提升学习性能（学习速度、精确度和泛化能力）；3）低增益要求确保了RTPL在实际应用中的鲁棒性。此外，基于RTPL的学习与控制将在任务执行过程中逐步相互增强，使其适用于长期学习控制任务。以RTPL作为自适应前馈控制器，用于解决一类非线性系统的跟踪控制问题。相应的理论分析与仿真研究验证了RTPL的有效性。