Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems with Input Nonlinearities

This paper proposes a back stepping controller for the class of discrete-time nonlinear system in the presence of input nonlinearities like saturation and dead-zone. A robust adaptive neural network (NN) control is investigated for a general class of uncertain single-input-single-output (SISO) discrete-time nonlinear systems with unknown system dynamics and input nonlinearities i.e. combination of saturation and dead-zone. For input nonlinearities, discrete-time SISO nonlinear system in combination with back stepping and Lyapunov synthesis is proposed for adaptive neural network design with guaranteed stability. The actuator nonlinearities are assumed to be unknown and compensated by a pre compensator using Chebyshev neural network (CNN) and unknown nonlinear functions are also approximated by CNN. Weight update laws, based on Lyapunov theory are derived to make this scheme adaptive and the convergence properties are shown. Simulation results validate the effectiveness of proposed scheme.