Adaptive neural network control of pure-feedback nonlinear discrete-time systems

Abstract

For a class of pure-feedback discrete-time nonlinear systems, adaptive neural network control based on backstepping design is proposed. To avoid the causality contradiction problem in backstepping design, the system is firstly transformed through a coordinate transformation. Then implicit function theorem is exploited to assert the existence of the desired virtual controls and practical control. By using high-order neural networks to approximate the desired controls, an effective adaptive neural network control system is developed by backstepping design. The closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation result illustrates the effectiveness of the proposed control.