A Radial Basis Function Neural Network approximator with fast terminal sliding mode-based learning algorithm and its application in control systems

This paper presents a new learning algorithm for Radial Basis Function Neural Networks (RBFNNs) in order to approximate unknown continuous functions. This algorithm is based on applying fast terminal sliding mode (FTSM) to the conventional gradient descent algorithm This makes faster convergence to the origin. Stability of the proposed algorithm is guaranteed by Lyapunov theorem. To demonstrate the accuracy and efficiency of our proposed methodology, we use it in control of Duffing system, through combining the proposed approximator with sliding mode control (SMC). The simulation results verify the benefits of the proposed scheme in approximation of unknown nonlinear continuous functions with increased convergence rate and less RMS error. Our proposed method has convergence time and RMS error value of about 2 seconds and 0.374 respectively while these values were 13 seconds and 0.625 for conventional method.