  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.
