A nonlinear adaptive controller using multiple models and neural network based on zero order proximity
boundedness for a class of single variable nonlinear discrete-time systems is proposed. The controller is consist of a nonlinear
robust adaptive controller and a nonlinear neural networks adaptive controller. These controllers can respectively guarantee
the stability of the system and improve the performance of the system when the restriction of nonlinear term is relaxed
to the zero order proximity boundedness. The control input can be generated by the action of the switching mechanism
between the two controllers. Finally, the stability and convergence of the system are proved, and simulation results validate
the effectiveness of proposed controllers.