Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time

In this paper, adaptive neural network (NN) control is investigated for a class of nonlinear pure-feedback discrete-time systems. By using prediction functions of future states, the pure-feedback system is transformed into an n-step-ahead predictor, based on which state feedback NN control is synthesized. Next, by investigating the relationship between outputs and states, the system is transformed into an input-output predictor model, and then, output feedback control is constructed. To overcome the difficulty of nonaffine appearance of the control input, implicit function theorem is exploited in the control design and NN is employed to approximate the unknown function in the control. In both state feedback and output feedback control, only a single NN is used and the controller singularity is completely avoided. The closed-loop system achieves semiglobal uniform ultimate boundedness (SGUUB) stability and the output tracking error is made within a neighborhood around zero. Simulation results are presented to show the effectiveness of the proposed control approach. Index Terms--Discrete-time system, neural network, pure-feedback system.