Selective Memory Recursive Least Squares (SMRLS) is a recursive least squares (RLS) based real-time training algorithm for linearly parameterized approximators. This project is a demo for radial basis function neural network (RBFNN) based real-time function approximation with SMRLS. The function of each file is explained as follows:

1. approximated_function.m -- used to set the function to be approximated by the RBFNN
2. RBFNN.m -- return the output of an RBFNN
3. centers.m -- used to set the neuron centers of the RBFNN
4. SMRLS.m -- SMRLS algorithm
5. VDFRLS.m -- variable-direction-forgetting RLS
6. FFRLS.m -- RLS with a constant forgetting factor
7. SGD.m -- stochastic gradient descent
8. randomnurbs.m & RandNurbs.m -- run 'randomnurbs.m' to generate a random non-uniform rational B-splines (NURBS) trajectory
9. sinusoidal.m -- used to generate a sinusoidal or spiral trajectory
10. main_sim.m -- main simulation program
11. plot_sim.m -- used to show the results
12. figure_plot.m -- used to generate detailed figures

To use this demo, it is recommended to run the program in the following order: randomnurbs.m/sinusoidal.m → main_sim.m → plot_sim.m