Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems via backstepping

The state feedback controller is studied for a class of strict-feedback discrete-time nonlinear systems in the presence of bounded disturbances. A Lyapunov-based full state feedback neural network control structure is presented via backstepping, which solves the noncausal problem in the discrete-time backstepping design procedure. The closed-loop system is proven to be semi-globally uniformly ultimately bounded. An arbitrarily small tracking error can be achieved if the size of the neural network is chosen large enough, and the control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.