Locally Reused Selective Memory RLS: Enhancing Real-Time Approximation via Partition-Based Memory Reinforcement

To address the problem of passive knowledge forgetting in real-time training of Radial Basis Function Neural Networks (RBFNNs), the Selective Memory Recursive Least Squares (SMRLS) algorithm was proposed to replace traditional forgetting with a spatial memory mechanism. However, SMRLS suffers from memory inertia, where weight updates lag behind abrupt system changes due to outdated memory in visited partitions. This paper proposes Locally Reused Selective Memory RLS (LR-SMRLS), which enhances SMRLS by reusing the most recent memory sample from the currently accessed partition multiple times during each update. This reinforcement retains fast learning speed and improves responsiveness to sudden changes while preserving the long-term memory structure. Simulation results demonstrate that LR-SMRLS achieves higher approximation accuracy and faster adaptation than existing methods, making it well-suited for real-time adaptive control applications.