Adaptive robust control based on single neural network approximation for a class of uncertain strict-feedback discrete-time nonlinear systems

In this paper, based on single neural network approximation, a novel adaptive robust control algorithm is proposed for a class of uncertain discrete-time nonlinear systems in the strict-feedback form. In order to solve the noncausal problem, the original system is transformed into a predictor form. Different from the existing methods for the investigated system, all unknown parts at internship steps are passed down in the discrete-time backstepping design procedure, and only one single neural network is used to approximate the lumped unknown function in the system at the last step. Following this approach, the designed controller contains only one actual control law and one adaptive law. Compared with the existing results for discrete-time systems, the proposed controller is simpler and the computational burden is lighter. The stability of the closed-loop system is proven to be uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero by choosing the control parameters appropriately. Simulation examples are employed to illustrate the effectiveness of the proposed approach.