Learning Control of Radial Basis Function Neural Network Based on Recursive Least Squares Update Law

Nonlinearities and uncertainties are common factors degrading the trajectory tracking performance of practical systems. With the development of neural networks, using them to learn nonlinear and uncertain factors into helpful information has become one of the most effective methods to solve this problem. Although traditional radial basis function neural network (RBFNN) learning control scheme with stochastic gradient descent (SGD) based update law can realize basic identification of uncertainties in closed-loop systems, it has unsatisfactory learning speed and accuracy. In order to improve the learning speed and accuracy of radial basis function neural networks, a recursive least squares (RLS) training method is proposed in this paper. An RLS based weight update law is derived from constructing a special Lyapunov function candidate. Theoretical analysis demonstrates the stability of the closed-loop system and convergence of the RBFNN weights with the persistent excitation (PE) condition. Related simulation results verify that RLS based RBFNN learning control has higher learning performance than the SGD-based algorithm.