An Improved RBFNN Controller for a Class of Nonlinear Discrete-Time Systems With Bounded Disturbance

Abstract

This chapter is concerned with an adaptive Radial basis function neural network (RBFNN) is studied and implemented for a class of nonlinear discrete-time system with bounded disturbance. Due to immeasurable states and presence of input-nonlinearities like backlash, dead zone and hystersis, the design of controller becomes more challenging. RBFNN is designed to the approximation of such nonlinear system at a relative degree of accuracy, which can be used for adaptation of nonlinear discrete-time systems with or without the presence of nonlinearities. RBFNN employs as a reference model which is useful to closed loop form of pure feedback controller. Based on Lyapunov method it is proven that proposed scheme for discrete-time nonlinear systems is asymptotically stable. Hence, not only stability of proposed system is assured but it is also shown that tracking error of model lies in closed neighborhood of zero. The feasibility of the RBFNN is demonstrated by two examples of nonlinear systems.