Direct RBF neural network control of a class of discrete-time non-affine nonlinear systems

Direct adaptive RBF NN control is presented for a class of discrete-time single-input single-output non-affine nonlinear systems. An implicit function theorem is used to prove the existence and uniqueness of the implicit desired feedback control. Based on the input-output model, RBF neural networks are used to emulate the implicit desired feedback control. The closed-loop is proven to be semi-globally uniformly ultimately bounded if the design parameters are suitably chosen under certain mild conditions. Simulation results show the effectiveness of the direct RBF neural network control.